Algebraic degree in spatial matricial numerical ranges of linear operators

2021 ◽  
Author(s):  
J. Bernik ◽  
L. Livshits ◽  
G. MacDonald ◽  
L. Marcoux ◽  
M. Mastnak ◽  
...  
Keyword(s):  
Hilbert Space ◽  
Unbounded Operator ◽  
Higher Order ◽  
Algebraic Degree ◽  
Linear Operators ◽  
Content Type

We study the maximal algebraic degree of principal ortho-compressions of linear operators that constitute spatial matricial numerical ranges of higher order. We demonstrate (amongst other things) that for a (possibly unbounded) operator L L on a Hilbert space, every principal m m -dimensional ortho-compression of L L has algebraic degree less than m m if and only if r a n k ( L − λ I ) ≤ m − 2 rank(L-\lambda I)\le m-2 for some λ ∈ C \lambda \in \mathbb {C} .

scholarly journals AN UNBOUNDED OPERATOR WITH SPECTRUM IN A STRIP AND MATRIX DIFFERENTIAL OPERATORS

2021 ◽  
pp. 1-8
Author(s):  
MICHAEL GIL’
Keyword(s):  
Hilbert Space ◽  
Unbounded Operator ◽  
Differential Operators ◽  
Bounded Operator ◽  
Linear Operators ◽  
Regular Matrix ◽  
Horizontal Strip ◽  
Matrix Differential Operators ◽  
Matrix Differential ◽  
Unbounded Linear Operators

Abstract Let A and $\tilde A$ be unbounded linear operators on a Hilbert space. We consider the following problem. Let the spectrum of A lie in some horizontal strip. In which strip does the spectrum of $\tilde A$ lie, if A and $\tilde A$ are sufficiently ‘close’? We derive a sharp bound for the strip containing the spectrum of $\tilde A$ , assuming that $\tilde A-A$ is a bounded operator and A has a bounded Hermitian component. We also discuss applications of our results to regular matrix differential operators.

Some properties of D-weak operator topology

2020 ◽  
Vol 70 (3) ◽  
pp. 753-758
Author(s):  
Marcel Polakovič
Keyword(s):  
Hilbert Space ◽  
Effect Algebra ◽  
Linear Subspace ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Weak Operator Topology ◽  
Generalized Effect Algebra ◽  
Weak Operator ◽  
Dense Linear Subspace

AbstractLet 𝓖D(𝓗) denote the generalized effect algebra consisting of all positive linear operators defined on a dense linear subspace D of a Hilbert space 𝓗. The D-weak operator topology (introduced by other authors) on 𝓖D(𝓗) is investigated. The corresponding closure of the set of bounded elements of 𝓖D(𝓗) is the whole 𝓖D(𝓗). The closure of the set of all unbounded elements of 𝓖D(𝓗) is also the set 𝓖D(𝓗). If Q is arbitrary unbounded element of 𝓖D(𝓗), it determines an interval in 𝓖D(𝓗), consisting of all operators between 0 and Q (with the usual ordering of operators). If we take the set of all bounded elements of this interval, the closure of this set (in the D-weak operator topology) is just the original interval. Similarly, the corresponding closure of the set of all unbounded elements of the interval will again be the considered interval.

scholarly journals Duality and the existence of weakly completely continuous elements in aB*-algebra

1972 ◽  
Vol 13 (1) ◽  
pp. 56-60 ◽  
Author(s):  
B. J. Tomiuk
Keyword(s):  
Hilbert Space ◽  
Left Ideal ◽  
Linear Operators ◽  
Completely Continuous ◽  
Identity Modulo

Ogasawara and Yoshinaga [9] have shown that aB*-algebra is weakly completely continuous (w.c.c.) if and only if it is*-isomorphic to theB*(∞)-sum of algebrasLC(HX), where eachLC(HX)is the algebra of all compact linear operators on the Hilbert spaceHx.As Kaplansky [5] has shown that aB*-algebra isB*-isomorphic to theB*(∞)-sum of algebrasLC(HX)if and only if it is dual, it follows that a5*-algebraAis w.c.c. if and only if it is dual. We have observed that, if only certain key elements of aB*-algebraAare w.c.c, thenAis already dual. This observation constitutes our main theorem which goes as follows.A B*-algebraAis dual if and only if for every maximal modular left idealMthere exists aright identity modulo M that isw.c.c.

Overcoming resistance to product rebranding

2015 ◽  
Vol 24 (6) ◽  
pp. 621-632 ◽  
Author(s):  
Véronique Collange ◽  
Adrien Bonache
Keyword(s):  
Indirect Effect ◽  
Consumer Attitudes ◽  
Higher Order ◽  
Brand Name ◽  
Negative Effects ◽  
Marketing Practice ◽  
Content Type ◽  
Name Change ◽  
Marketing Managers ◽  
The Impact

Purpose – The purpose of this article is to understand how and why consumers resist or accept product rebranding. It seeks to identify and to quantify the drivers of attitudes toward this marketing practice to guide marketing managers in the execution of an effective changeover. Design/methodology/approach – The research is conducted in three stages. First, a qualitative study is run among 45 consumers to identify variables that might influence attitudes toward product rebranding. Second, a review of literature on the emotion of surprise is carried out to specify the relationships between the variables previously identified and to formulate hypotheses. Third, a quantitative study is conducted among 480 consumers to test the hypotheses and to quantify the impact of each variable. Findings – Surprise impacts attitudes toward product rebranding through a three-way process (automatic, higher-order cognitive, higher-order affective): a direct negative effect, an indirect effect mediated by incomprehension about the reasons for the change and an indirect effect mediated by the negative emotions generated by the change. Moreover, trust in firms diminishes the negative effects of anger, fear and sadness on attitudes toward product rebranding. Research limitations/implications – The research offers a better understanding of processes involved in the building of consumer attitudes toward brand name change. However, it only constitutes a first step in the attempt to understand the phenomena. Practical implications – This practice of brand name change is increasingly popular, but marketing managers are skeptical about the best way to implement it. The paper provides a better understanding of consumer reactions to product rebranding, so that marketing managers can make better decisions. It reveals guidance for successful brand name changes. Originality/value – This paper is the first to propose and to test a comprehensive model of the mental processes involved in the building of consumer attitudes toward product rebranding.

scholarly journals The numerical ranges of unbounded linear operators

1975 ◽  
Vol 12 (1) ◽  
pp. 23-25 ◽  
Author(s):  
Béla Bollobás ◽  
Stephan E. Eldridge
Keyword(s):  
Banach Space ◽  
Scalar Field ◽  
Banach Spaces ◽  
Unbounded Operator ◽  
Numerical Range ◽  
Linear Operators ◽  
Density Property ◽  
Unbounded Linear Operators

Giles and Joseph (Bull. Austral. Math. Soc. 11 (1974), 31–36), proved that the numerical range of an unbounded operator on a Banach space has a certain density property. They showed, in particular, that the numerical range of an unbounded operator on certain Banach spaces is dense in the scalar field. We prove that the numerical range of an unbounded operator on a Banach space is always dense in the scalar field.

The role of service fairness in the service quality – relationship quality – customer loyalty chain

2015 ◽  
Vol 25 (6) ◽  
pp. 744-776 ◽  
Author(s):  
Apostolos Giovanis ◽  
Pinelopi Athanasopoulou ◽  
Evangelos Tsoukatos
Keyword(s):  
Service Quality ◽  
Relationship Quality ◽  
Customer Loyalty ◽  
Higher Order ◽  
Equation Modeling ◽  
Content Type ◽  
Order Construct ◽  
Service Fairness

Purpose – The purpose of this paper is to extend the well-established nomological network of service quality-relationship quality-customer loyalty by introducing service fairness – a distinct service evaluation concept. Specifically, the study aims to investigate the impact of service fairness on relationship quality as a complementary to service quality driver, and the direct and indirect effect of service fairness on customer loyalty in the presence of service quality and relationship quality in a no failure/recovery effort service context. Design/methodology/approach – A telephone survey of a random sample of 408 customers of auto repair and maintenance services was implemented using a structured questionnaire with established scales. Data were analyzed with partial least squares path methodology, a structural equation modeling methodology. Findings – Interactional fairness is the most important formative determinant of customers’ overall fairness perception, followed by procedural and distributive fairness. Relationship quality measured as a higher order construct, made of satisfaction; trust; affective and calculative commitment, is the main determinant of customer loyalty. Also, it partially mediates, along with service quality, the relationship between service fairness and customer loyalty and fully mediates the effect of service quality on customer loyalty. Finally, service fairness has the highest overall effect on customer loyalty. Research limitations/implications – The sample is industry-specific and this may affect generalizability of findings. Also, the cross-sectional design adopted does not reflect temporal changes. Practical implications – Interactional fairness is of utmost importance to customers of the investigated industry. So, customers should be fairly treated at every point of contact. Also, service quality is heavily affected by service fairness. Thus, fair service leads to high-perceived service quality. Third, service quality affects customer loyalty only through relationship quality. Only when service quality is coupled by long-term quality relationships, signs of customer loyalty appear. Finally, service fairness influences customer loyalty mainly through service and relationship quality and has the highest overall effect on customer loyalty. So, fairly treating customers is crucial for developing long-term relationships that lead to customer loyalty. Originality/value – The role of service fairness in the service quality-relationship quality-customer loyalty chain is investigated and using a higher order construct for relationship quality.

scholarly journals Distinct Mechanism for the Formation of the Ribonucleoprotein Complex of Tomato Spotted Wilt Virus

2017 ◽  
Vol 91 (23) ◽  
Author(s):  
Yu Guo ◽  
Baocheng Liu ◽  
Zhenzhen Ding ◽  
Guobang Li ◽  
Meizi Liu ◽  
...  
Keyword(s):  
Tomato Spotted Wilt Virus ◽  
Higher Order ◽  
The Body ◽  
Full Length ◽  
Content Type ◽  
Ribonucleoprotein Complex ◽  
Tomato Spotted Wilt ◽  
Distinct Mechanism ◽  
C Terminus ◽  
Wilt Virus

ABSTRACT The Tomato spotted wilt virus (TSWV) belongs to the Tospovirus genus of the Bunyaviridae family and represents the sole plant-infecting group within bunyavirus. TSWV encodes a nucleocapsid protein (N) which encapsidates the RNA genome to form a ribonucleoprotein complex (RNP). In addition, the N has multiple roles during the infection of plant cells. Here, we report the crystal structure of the full-length TSWV N. The N features a body domain consisting of an N-lobe and a C-lobe. These lobes clamp a positively charged groove which may constitute the RNA binding site. Furthermore, the body domains are flanked by N- and C-terminal arms which mediate homotypic interactions to the neighboring subunits, resulting in a ring-shaped N trimer. Interestingly, the C terminus of one protomer forms an additional interaction with the protomer of an adjacent trimer in the crystal, which may constitute a higher-order oligomerization contact. In this way, this study provides insights into the structure and trimeric assembly of TSWV N, which help to explain previous functional findings, but also suggests distinct N interactions within a higher-order RNP. IMPORTANCE TSWV is one of the most devastating plant pathogens that cause severe diseases in numerous agronomic and ornamental crops worldwide. TSWV is also the prototypic member of the Tospovirus genus, which is the sole group of plant-infecting viruses in the bunyavirus family. This study determined the structure of full-length TSWV N in an oligomeric state. The structural observations explain previously identified biological properties of TSWV N. Most importantly, the additional homotypic interaction between the C terminus of one protomer with another protomer indicates that there is a distinct mechanism of RNP formation in the bunyavirus family, thereby enhancing the current knowledge of negative-sense single-stranded RNA virus-encoded N. TSWV N is the last remaining representative N with an unknown structure in the bunyavirus family. Combined with previous studies, the structure of TSWV N helps to build a complete picture of the bunyavirus-encoded N family and reveals a close evolutionary relationship between orthobunyavirus, phlebovirus, hantavirus, and tospovirus.

Sign in / Sign up

Export Citation Format

Share Document