Displaying similar documents to “A note on a theorem of Vidav”

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.

The inclusion theorem for multiple summing operators

David Pérez-García (2004)

Studia Mathematica

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We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.

Squaring a reverse AM-GM inequality

Minghua Lin (2013)

Studia Mathematica

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Let A, B be positive operators on a Hilbert space with 0 < m ≤ A, B ≤ M. Then for every unital positive linear map Φ, Φ²((A + B)/2) ≤ K²(h)Φ²(A ♯ B), and Φ²((A+B)/2) ≤ K²(h)(Φ(A) ♯ Φ(B))², where A ♯ B is the geometric mean and K(h) = (h+1)²/(4h) with h = M/m.

A class of generalized-Hilbert-Schmidt operators

B. E. Rhoades (1975)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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G. H. Constantin ha definito una classe di operatori di Cesàro-Hilbert-Schmidt. In questa Nota l'Autore trova la corrispondente proprietà per una più generale classe di operatori di Hilbert-Schmidt (G. H. S.).

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.

Separate and joint similarity to families of normal operators

Piotr Niemiec (2002)

Studia Mathematica

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Sets of bounded linear operators , ⊂ ℬ(H) (ℋ is a Hilbert space) are similar if there exists an invertible (in ℬ(H)) operator G such that G - 1 · · G = . A bounded operator is scalar if it is similar to a normal operator. is jointly scalar if there exists a set ⊂ ℬ(H) of normal operators such that and are similar. is separately scalar if all its elements are scalar. Some necessary and sufficient conditions for joint scalarity of a separately scalar abelian set of Hilbert space operators are presented...

Logarithmic concavity, unitarity and selfadjointness

Jan Stochel (2005)

Banach Center Publications

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Isometric automorphisms of normed linear spaces are characterized by suitable concavity properties of powers of operators. Bounded selfadjoint operators in Hilbert spaces are described by parallel concavity properties of the exponential group. Unbounded infinitesimal generators of 𝓒₀-groups of Hilbert space operators having concavity properties are characterized as well.