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### ${}^{\infty }$-vectors and boundedness

Annales Polonici Mathematici

The following two questions as well as their relationship are studied: (i) Is a closed linear operator in a Banach space bounded if its ${}^{\infty }$-vectors coincide with analytic (or semianalytic) ones? (ii) When are the domains of two successive powers of the operator in question equal? The affirmative answer to the first question is established in case of paranormal operators. All these investigations are illustrated in the context of weighted shifts.

### A Fuglede-Putnam theorem modulo the Hilbert-Schmidt class for almost normal operators with finite modulus of Hilbert-Schmidt quasi-triangularity

Concrete Operators

We extend the Fuglede-Putnam theorem modulo the Hilbert-Schmidt class to almost normal operators with finite Hilbert-Schmidt modulus of quasi-triangularity.

### A function-theoretic proof of a theorem of Stampfli

Colloquium Mathematicae

### A new characterization of Anderson’s inequality in ${C}_{1}$-classes

Czechoslovak Mathematical Journal

Let $ℋ$ be a separable infinite dimensional complex Hilbert space, and let $ℒ\left(ℋ\right)$ denote the algebra of all bounded linear operators on $ℋ$ into itself. Let $A=\left({A}_{1},{A}_{2},\cdots ,{A}_{n}\right)$, $B=\left({B}_{1},{B}_{2},\cdots ,{B}_{n}\right)$ be $n$-tuples of operators in $ℒ\left(ℋ\right)$; we define the elementary operators ${\Delta }_{A,B}\phantom{\rule{0.222222em}{0ex}}ℒ\left(ℋ\right)↦ℒ\left(ℋ\right)$ by ${\Delta }_{A,B}\left(X\right)={\sum }_{i=1}^{n}{A}_{i}X{B}_{i}-X.$ In this paper, we characterize the class of pairs of operators $A,B\in ℒ\left(ℋ\right)$ satisfying Putnam-Fuglede’s property, i.e, the class of pairs of operators $A,B\in ℒ\left(ℋ\right)$ such that ${\sum }_{i=1}^{n}{B}_{i}T{A}_{i}=T$ implies ${\sum }_{i=1}^{n}{A}_{i}^{*}T{B}_{i}^{*}=T$ for all $T\in {𝒞}_{1}\left(ℋ\right)$ (trace class operators). The main result is the equivalence between this property and the fact that...

### A note on $\left({𝒞}_{p},\alpha \right)$-hyponormal operators.

Journal of Inequalities and Applications [electronic only]

### A note on subnormal operators

Matematički Vesnik

### A note on the range of the operator $X↦TX-XT$ defined on ${𝒞}_{2}\left(ℋ\right)$.

International Journal of Mathematics and Mathematical Sciences

### A quasi-affine transform of an unbounded operator

Studia Mathematica

Some results on quasi-affinity for bounded operators are extended to unbounded ones and normal extensions of an unbounded operator are discussed in connection with quasi-affinity.

### A remark concerning Putinar's model of hyponormal weighted shifts

Czechoslovak Mathematical Journal

The question whether a hyponormal weighted shift with trace class self-commutator is the compression modulo the Hilbert-Schmidt class of a normal operator, remains open. It is natural to ask whether Putinar's construction through which he proved that hyponormal operators are subscalar operators provides the answer to the above question. We show that the normal extension provided by Putinar's theory does not lead to the extension that would provide a positive answer to the question.

### A remark on the range of elementary operators

Czechoslovak Mathematical Journal

Let $L\left(H\right)$ denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space $H$ into itself. Given $A\in L\left(H\right)$, we define the elementary operator ${\Delta }_{A}:L\left(H\right)⟶L\left(H\right)$ by ${\Delta }_{A}\left(X\right)=AXA-X$. In this paper we study the class of operators $A\in L\left(H\right)$ which have the following property: $ATA=T$ implies $A{T}^{*}A={T}^{*}$ for all trace class operators $T\in {C}_{1}\left(H\right)$. Such operators are termed generalized quasi-adjoints. The main result is the equivalence between this character and the fact that the ultraweak closure of the range of ${\Delta }_{A}$ is closed under taking...

### A Strict Maximum Modulus Theorem for Certain Banach Spaces.

Monatshefte für Mathematik

### Absolute continuity and hyponormal operators.

International Journal of Mathematics and Mathematical Sciences

### Absolutely summing operators and measure amarts in Fréchet spaces

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications

### Acotabilidad de la función resolvente local.

Extracta Mathematicae

### Aluthge transforms of $\left({C}_{p};\alpha \right)$-hyponormal operators.

Annals of Functional Analysis (AFA) [electronic only]

### An Extension of Putnam-Fuglede Theorem for Hyponormal Operators.

Mathematische Zeitschrift

### An inequality for spherical Cauchy dual tuples

Colloquium Mathematicae

Let T be a spherical 2-expansive m-tuple and let ${T}^{}$ denote its spherical Cauchy dual. If ${T}^{}$ is commuting then the inequality $\genfrac{}{}{0pt}{}{{\sum }_{|\beta |=k}{\left(\beta !\right)}^{-1}{\left({T}^{}\right)}^{\beta }\left({T}^{}\right){*}^{\beta }\le \left(k+m-1}{k\right){\sum }_{|\beta |=k}{\left(\beta !\right)}^{-1}\left({T}^{}\right){*}^{\beta }{\left({T}^{}\right)}^{\beta }}$ holds for every positive integer k. In case m = 1, this reveals the rather curious fact that all positive integral powers of the Cauchy dual of a 2-expansive (or concave) operator are hyponormal.

### An operator-theoretic approach to truncated moment problems

Banach Center Publications

We survey recent developments in operator theory and moment problems, beginning with the study of quadratic hyponormality for unilateral weighted shifts, its connections with truncated Hamburger, Stieltjes, Hausdorff and Toeplitz moment problems, and the subsequent proof that polynomially hyponormal operators need not be subnormal. We present a general elementary approach to truncated moment problems in one or several real or complex variables, based on matrix positivity and extension. Together...

### Another version of Anderson's inequality in the ideal of all compact operators.

JIPAM. Journal of Inequalities in Pure &amp; Applied Mathematics [electronic only]

### Approximation the Shift with Toeplitz Operators.

Mathematische Zeitschrift

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