Displaying similar documents to “Characterizations of subnormal operators”

A remark concerning Putinar's model of hyponormal weighted shifts

Vasile Lauric (2018)

Czechoslovak Mathematical Journal

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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. ...

Exponentials of normal operators and commutativity of operators: a new approach

Mohammed Hichem Mortad (2011)

Colloquium Mathematicae

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We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some results on similarities by Berberian and Embry as well as the celebrated Fuglede theorem.

Commutativity of compact selfadjoint operators

G. Greiner, W. Ricker (1995)

Studia Mathematica

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The relationship between the joint spectrum γ(A) of an n-tuple A = ( A 1 , . . . , A n ) of selfadjoint operators and the support of the corresponding Weyl calculus T(A) : f ↦ f(A) is discussed. It is shown that one always has γ(A) ⊂ supp (T(A)). Moreover, when the operators are compact, equality occurs if and only if the operators A j mutually commute. In the non-commuting case the equality fails badly: While γ(A) is countable, supp(T(A)) has to be an uncountable set. An example is given showing that, for non-compact...

The complete hyperexpansivity analog of the Embry conditions

Ameer Athavale (2003)

Studia Mathematica

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The Embry conditions are a set of positivity conditions that characterize subnormal operators (on Hilbert spaces) whose theory is closely related to the theory of positive definite functions on the additive semigroup ℕ of non-negative integers. Completely hyperexpansive operators are the negative definite counterpart of subnormal operators. We show that completely hyperexpansive operators are characterized by a set of negativity conditions, which are the natural analog of the Embry conditions...

Backward extensions of hyperexpansive operators

Zenon J. Jabłoński, Il Bong Jung, Jan Stochel (2006)

Studia Mathematica

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The concept of k-step full backward extension for subnormal operators is adapted to the context of completely hyperexpansive operators. The question of existence of k-step full backward extension is solved within this class of operators with the help of an operator version of the Levy-Khinchin formula. Some new phenomena in comparison with subnormal operators are found and related classes of operators are discussed as well.

Backward Aluthge iterates of a hyponormal operator and scalar extensions

C. Benhida, E. H. Zerouali (2009)

Studia Mathematica

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Let R and S be two operators on a Hilbert space. We discuss the link between the subscalarity of RS and SR. As an application, we show that backward Aluthge iterates of hyponormal operators and p-quasihyponormal operators are subscalar.