scholarly journals On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 212
Author(s):  
Chunji Li ◽  
Cheon Ryoo
Keyword(s):  
Sufficient Conditions ◽  
Weighted Shift ◽  
Weighted Sequence ◽  
Unilateral Weighted Shift

Let 1 < a < b < c < d and α ^ 5 : = 1 , a , b , c , d ∧ be a weighted sequence that is recursively generated by five weights 1 , a , b , c , d . In this paper, we give sufficient conditions for the positive quadratic hyponormalities of W α x and W α y , x , with α x : x , α ^ 5 and α y , x : y , x , α ^ 5 .

scholarly journals On linear operators and bases on Köthe spaces

2016 ◽  
Vol 1 (2) ◽  
pp. 617-624 ◽  
Author(s):  
M. Maldonado ◽  
J. Prada ◽  
M. J. Senosiain
Keyword(s):  
Analytic Functions ◽  
Generalized Derivation ◽  
Weighted Shift ◽  
Linear Operators ◽  
Shift Operators ◽  
Köthe Spaces ◽  
Unilateral Weighted Shift ◽  
Spaces Of Analytic Functions

AbstractWe make a survey of results published by the authors about the backward and forward unilateral weighted shift operators in Kóthe spaces, the so-called generalized derivation and integration operators, extending well-known results for spaces of analytic functions.

BACKWARD 3-STEP EXTENSIONS OF RECURSIVELY GENERATED WEIGHTED SHIFTS: A RANGE OF QUADRATIC HYPONORMALITY

2013 ◽  
Vol 89 (3) ◽  
pp. 488-493
Author(s):  
GEORGE R. EXNER ◽  
IL BONG JUNG ◽  
MI RYEONG LEE ◽  
SUN HYUN PARK
Keyword(s):  
Open Problem ◽  
Weighted Shift ◽  
Real Numbers ◽  
Weighted Shifts ◽  
Positive Real ◽  
Weight Sequence ◽  
Weighted Sequence ◽  
Quadratically Hyponormal

AbstractLet $\alpha : 1, 1, \sqrt{x} , \mathop{( \sqrt{u} , \sqrt{v} , \sqrt{w} )}\nolimits ^{\wedge } $ be a backward 3-step extension of a recursively generated weighted sequence of positive real numbers with $1\leq x\leq u\leq v\leq w$ and let ${W}_{\alpha } $ be the associated weighted shift with weight sequence $\alpha $. The set of positive real numbers $x$ such that ${W}_{\alpha } $ is quadratically hyponormal for some $u, v$ and $w$ is described, solving an open problem due to Curto and Jung [‘Quadratically hyponormal weighted shifts with two equal weights’, Integr. Equ. Oper. Theory 37 (2000), 208–231].

Dynamics of Operator-Weighted Shifts

2019 ◽  
Vol 29 (08) ◽  
pp. 1950110 ◽  
Author(s):  
Zongbin Yin ◽  
Yuming Chen ◽  
Qiaomin Xiang
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Weighted Shift ◽  
Necessary And Sufficient Conditions ◽  
Weighted Shifts ◽  
Diagonal Operators ◽  
Weight Sequence ◽  
Necessary And Sufficient

This paper investigates the dynamics of bilateral operator-weighted shifts on [Formula: see text] with a weight sequence of positive diagonal operators on a Hilbert space [Formula: see text]. Necessary and sufficient conditions for the bilateral weighted shifts to be hypercyclic (subspace-hypercyclic, frequently hypercyclic, Devaney chaotic, respectively) are provided. As a consequence, it is shown that for any [Formula: see text]-set [Formula: see text] of positive numbers which is bounded and bounded away from zero, there exists an invertible bilateral operator-weighted shift [Formula: see text] such that [Formula: see text]. Furthermore, the (hereditary) Cesàro-hypercyclicity of the bilateral weighted shifts is characterized.

scholarly journals A quantitative interpretation of the frequent hypercyclicity criterion

2017 ◽  
Vol 39 (4) ◽  
pp. 898-924 ◽  
Author(s):  
ROMUALD ERNST ◽  
AUGUSTIN MOUZE
Keyword(s):  
Weighted Shift ◽  
Quantitative Interpretation ◽  
Hypercyclicity Criterion ◽  
Unilateral Weighted Shift

We give a quantitative interpretation of the frequent hypercyclicity criterion. Actually we show that an operator which satisfies the frequent hypercyclicity criterion is necessarily $A$-frequently hypercyclic, where $A$ refers to some weighted densities sharper than the natural lower density. In that order, we exhibit different scales of weighted densities that are of interest to quantify the ‘frequency’ measured by the frequent hypercyclicity criterion. Moreover, we construct an example of a unilateral weighted shift which is frequently hypercyclic but not $A$-frequently hypercyclic on a particular scale.

scholarly journals Subnormality of Powers of Multivariable Weighted Shifts

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Sang Hoon Lee ◽  
Woo Young Lee ◽  
Jasang Yoon
Keyword(s):  
Hilbert Space ◽  
Open Problem ◽  
Operator Theory ◽  
Sufficient Conditions ◽  
Weighted Shift ◽  
Necessary And Sufficient Conditions ◽  
Weighted Shifts ◽  
Hilbert Space Operators ◽  
Necessary And Sufficient

Given a pair T ≡ T 1 , T 2 of commuting subnormal Hilbert space operators, the Lifting Problem for Commuting Subnormals (LPCS) asks for necessary and sufficient conditions for the existence of a commuting pair N ≡ N 1 , N 2 of normal extensions of T 1 and T 2 ; in other words, T is a subnormal pair. The LPCS is a longstanding open problem in the operator theory. In this paper, we consider the LPCS of a class of powers of 2 -variable weighted shifts. Our main theorem states that if a “corner” of a 2-variable weighted shift T = W α , β ≔ T 1 , T 2 is subnormal, then T is subnormal if and only if a power T m , n ≔ T 1 m , T 2 n is subnormal for some m , n ≥ 1 . As a corollary, we have that if T is a 2-variable weighted shift having a tensor core or a diagonal core, then T is subnormal if and only if a power of T is subnormal.

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

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