scholarly journals On a class of operators with normal Aluthge transformations

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 969-975
Author(s):  
Yousef Estaremi
Keyword(s):  
Large Class ◽  
Point Spectrum ◽  
Hölder Inequality ◽  
Weak Condition ◽  
Joint Point ◽  
Concrete Application ◽  
Joint Point Spectrum

In this paper, we show that the generalized Aluthge transformations of a large class of operators (weighted conditional type operators) are normal. As a consequence, the operatorMwEMu is p-hyponormal if and only if it is normal, and under a weak condition, if MwEMu is normal, then the Holder inequality turn into equality for w; u. Also, we give some applications of p-hyponormal weighted conditional type operators, for instance, point spectrum and joint point spectrum of p-hyponormal weighted conditional type operators are equal. In the end, some examples are provided to illustrate concrete application of the main results of the paper.

scholarly journals On a class of operators with normal Aluthge transformations

Filomat ◽  
2015 ◽  
Vol 29 (8) ◽  
pp. 1789-1794 ◽  
Author(s):  
Yousef Estaremi
Keyword(s):  
Large Class ◽  
Point Spectrum ◽  
Hölder Inequality ◽  
Weak Condition ◽  
Joint Point ◽  
Concrete Application ◽  
Joint Point Spectrum ◽  
Font Color

In this paper, we show that the generalized Aluthge transformations of a large class of operators (weighted conditional type operators) are normal. As a consequence, the operatorMwEMu is p-hyponormal if and only if it is normal, and under a weak condition, if MwEMu is normal, then the Holder inequality turn into equality for w; u. Also, we give some applications of p-hyponormal weighted conditional type operators, for instance, point spectrum and joint point spectrum of p-hyponormal weighted conditional type operators are equal. In the end, some examples are provided to illustrate concrete application of the main results of the paper. <br><br><font color="red"><b> This article has been retracted. Link to the retraction <u><a href="http://dx.doi.org/10.2298/FIL1601253E">10.2298/FIL1601253E</a><u></b></font>

scholarly journals On the joint spectra of doubly commuting n-tuples of semi-normal operators

1985 ◽  
Vol 26 (1) ◽  
pp. 47-50 ◽  
Author(s):  
Muneo Chō ◽  
A. T. Dash
Keyword(s):  
Point Spectrum ◽  
Complex Hilbert Space ◽  
Bounded Linear ◽  
Approximate Point Spectrum ◽  
Joint Point ◽  
Normal Operators ◽  
Definition Of ◽  
Image Position ◽  
Joint Point Spectrum ◽  
Unit Vectors

Let H be a complex Hilbert space. For any operator (bounded linear transformation) T on H, we denote the spectrum of T by σ(T). Let T = (T1, …, Tn) be an n-tuple of commuting operators on H. Let Sp(T) be the Taylor joint spectrum of T. We refer the reader to [8] for the definition of Sp(T). A point v = (v1, …, vn) of ℂn is in the joint approximate point spectrum σπ(T) of T if there exists a sequence {xk} of unit vectors in H such that.A point v = (v1, …, vn) of ℂn is in the joint approximate compression spectrum σs(T) of T if there exists a sequence {xk} of unit vectors in H such thatA point v=(v1, …, vn) of ℂn is in the joint point spectrum σp(T) of T if there exists a non-zero vector x in H such that (Ti-vi)x = 0 for all i, 1 ≤ j ≤ n.

scholarly journals Spectrum of Quasi-Class (A,k) Operators

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Xiaochun Li ◽  
Fugen Gao ◽  
Xiaochun Fang
Keyword(s):  
Positive Integer ◽  
Invariant Subspace ◽  
Spectral Properties ◽  
Point Spectrum ◽  
Approximate Point Spectrum ◽  
Common Generalization ◽  
Class A ◽  
Joint Point ◽  
Joint Point Spectrum

An operator T∈B(ℋ) is called quasi-class (A,k) if T∗k(|T2|−|T|2)Tk≥0 for a positive integer k, which is a common generalization of class A. In this paper, firstly we consider some spectral properties of quasi-class (A,k) operators; it is shown that if T is a quasi-class (A,k) operator, then the nonzero points of its point spectrum and joint point spectrum are identical, the eigenspaces corresponding to distinct eigenvalues of T are mutually orthogonal, and the nonzero points of its approximate point spectrum and joint approximate point spectrum are identical. Secondly, we show that Putnam's theorems hold for class A operators. Particularly, we show that if T is a class A operator and either σ(|T|) or σ(|T∗|) is not connected, then T has a nontrivial invariant subspace.

scholarly journals Spectrum of class absolute -*-k-paranormal operators for 0 ≤ k ≤ 1

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 671-678
Author(s):  
Changsen Yang ◽  
Junli Shen
Keyword(s):  
Point Spectrum ◽  
Open Neighborhood ◽  
Norm Inequality ◽  
Operator Inequality ◽  
Inclusion Relation ◽  
Approximate Point Spectrum ◽  
New Class ◽  
Joint Point ◽  
Weyl Spectrum ◽  
Joint Point Spectrum

In this paper, we shall introduce a new class absolute-*-k-paranormal operators given by a norm inequality and *-A(k) operator by operator inequality, we will discuss the inclusion relation of them. And we study spectral properties of class absolute-*-k-paranormal operators. We show that if T belongs to class absolute-*-k-paranormal operators, then its point spectrum and joint point spectrum are identical, its approximate point spectrum and joint approximate point spectrum are identical. Next as an application of them, for Weyl spectrum w(?) and essential approximate point spectrum ?ea, (?), we will show that if T or T*is absolute-*-k-paranormal for 0 ? k ? 1, then w(f (T)) = ? (w(T)), ?ea(? (T)) = ?(?ea(T)) for every ? ?? H(?(T)) where H(?(T)) denotes the set of all analytic functions on an open neighborhood of ?(T).

scholarly journals Asymptotic escape rates and limiting distributions for multimodal maps

2020 ◽  
pp. 1-50
Author(s):  
MARK F. DEMERS ◽  
MIKE TODD
Keyword(s):  
Variational Principle ◽  
Invariant Measure ◽  
Large Class ◽  
Open Systems ◽  
Periodic Points ◽  
Weak Condition ◽  
Escape Rate ◽  
Scaling Limits ◽  
Absolutely Continuous ◽  
Initial Distributions

We consider multimodal maps with holes and study the evolution of the open systems with respect to equilibrium states for both geometric and Hölder potentials. For small holes, we show that a large class of initial distributions share the same escape rate and converge to a unique absolutely continuous conditionally invariant measure; we also prove a variational principle connecting the escape rate to the pressure on the survivor set, with no conditions on the placement of the hole. Finally, introducing a weak condition on the centre of the hole, we prove scaling limits for the escape rate for holes centred at both periodic and non-periodic points, as the diameter of the hole goes to zero.

Spectral Theory for the Neumann Laplacian on Planar Domains With Horn-Like Ends

1997 ◽  
Vol 49 (2) ◽  
pp. 232-262 ◽  
Author(s):  
Julian Edward
Keyword(s):  
Large Class ◽  
Continuous Spectrum ◽  
Spectral Theory ◽  
Point Spectrum ◽  
Pure Point ◽  
Pure Point Spectrum ◽  
Singular Continuous Spectrum ◽  
Finite Multiplicity ◽  
Planar Domains ◽  
Neumann Laplacian

AbstractThe spectral theory for the Neumann Laplacian on planar domains with symmetric, horn-like ends is studied. For a large class of such domains, it is proven that the Neumann Laplacian has no singular continuous spectrum, and that the pure point spectrum consists of eigenvalues of finite multiplicity which can accumulate only at 0 or ∞. The proof uses Mourre theory.

scholarly journals A MIXED MULTIFRACTAL ANALYSIS FOR QUASI-AHLFORS VECTOR-VALUED MEASURES

Fractals ◽  
2021 ◽  
pp. 2240001
Author(s):  
ANOUAR BEN MABROUK ◽  
ADEL FARHAT
Keyword(s):  
Large Class ◽  
Multifractal Analysis ◽  
Weak Condition ◽  
Probability Measures ◽  
Original Formulation ◽  
Multifractal Formalism ◽  
Self Similar ◽  
Joint Multifractal Analysis ◽  
Vector Valued ◽  
Special Classes

The multifractal formalism for measures in its original formulation is checked for special classes of measures, such as, doubling, self-similar, and Gibbs-like ones. Out of these classes, suitable conditions should be taken into account to prove the validity of the multifractal formalism. In this work, a large class of measures satisfying a weak condition known as quasi-Ahlfors is considered in the framework of mixed multifractal analysis. A joint multifractal analysis of finitely many quasi-Ahlfors probability measures is developed. Mixed variants of multifractal generalizations of Hausdorff, and packing measures, and corresponding dimensions are introduced. By applying convexity arguments, some properties of these measures, and dimensions are established. Finally, an associated multifractal formalism is introduced, and proved to hold for the class of quasi-Ahlfors measures. Besides, some eventual applications, and motivations, especially, in AI are discussed.

A Large Class of p-Ary Cyclic Codes and Sequence Families

2010 ◽  
Vol E93-A (11) ◽  
pp. 2272-2277
Author(s):  
Zhengchun ZHOU ◽  
Xiaohu TANG ◽  
Udaya PARAMPALLI
Keyword(s):  
Large Class ◽  
Cyclic Codes

The Social Furniture of Virtual Worlds

Disputatio ◽  
2019 ◽  
Vol 11 (55) ◽  
pp. 345-369
Author(s):  
Peter Ludlow
Keyword(s):  
Large Class ◽  
Data Structures ◽  
Virtual Worlds ◽  
Causal Powers ◽  
Virtual Objects ◽  
David Chalmers ◽  
The Social

AbstractDavid Chalmers argues that virtual objects exist in the form of data structures that have causal powers. I argue that there is a large class of virtual objects that are social objects and that do not depend upon data structures for their existence. I also argue that data structures are themselves fundamentally social objects. Thus, virtual objects are fundamentally social objects.

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