The Norm of a Hermitian Element in a Banach Algebra

Sinclair, A. M.

doi:10.2307/2037989

Cited by 10 publications

(12 citation statements)

References 1 publication

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“…For example, if T is a Hermitian operator, then T = r(T ), where r(T ) is the spectral radius of T . This was proved by Browder [7], Katznelson [14] and Sinclair [23]. All the three proofs depend on Bernstein's inequality.…”

Section: An Operator T ∈ B(x) Is Said To Be Hermitian If V (T ) Is Rementioning

confidence: 87%

Dissipative operators on Banach spaces

Mustafayev¹

2007

Journal of Functional Analysis

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Section: An Operator T ∈ B(x) Is Said To Be Hermitian If V (T ) Is Rementioning

confidence: 87%

Dissipative operators on Banach spaces

Mustafayev¹

2007

Journal of Functional Analysis

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“…It is well-known that the operator norm of a selfadjoint operator in a Hilbert space coincides with its spectral radius. Making use of the Bernstein inequality, Katsnelson proved in [17] the following result, which, independently (and more or less simultaneously), was also found by Browder [4] and Sinclair [39]. Theorem 4.1.…”

Section: Series Of Simple Fractionsmentioning

confidence: 77%

A piece of Victor Katsnelson's mathematical biography

Sodin¹

2019

Preprint

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We give an overview of several works of Victor Katsnelson published in 1965-1970, and pertaining to the complex and harmonic analysis and the spectral theory. A preambleAs a mathematician, Victor Katsnelson was raised within a fine school of function theory and functional analysis, which was blossoming in Kharkov starting the second half of 1930s. He studied in the Kharkov State University in 1960-1965. Among his teachers were Naum Akhiezer, Boris Levin, Vladimir Marchenko. That time he became acquainted with Vladimir Matsaev whom Victor often mentions as one of his teachers. In 1965 Katsnelson graduated with the master degree, Boris Levin supervised his master thesis. Since then and till 1990, he teaches at the Department of Mathematics and Mechanics of the Kharkov State University. In 1967 he defends the PhD Thesis "Convergence and Summability of Series in Root Vectors of Some Classes of Non-Selfadjoint Operators" also written under Boris Levin guidance. Until he left Kharkov in the early 1990s, Katsnelson remained an active participant of the Kharkov function theory seminar run on Thursdays by Boris Levin and IossifOstrovskii. His talks, remarks and questions were always interesting and witty.

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“…For details of this result and those quoted above the reader is referred to [7,36]. The connection between the results quoted above and partially ordered real Banach spaces is described in the next lemma.…”

Section: Lemma 22mentioning

confidence: 81%

The Banach–Lie algebra of multiplication operators on a JBW∗-triple

Altwaijry¹,

Edwards²

2008

Journal of Functional Analysis

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The Banach-Lie algebra L(A) of multiplication operators on the JB * -triple A is introduced and it is shown that the hermitian part L(A) h of L(A) is a unital GM-space the base of the dual cone in the dual GL-space (L(A) h ) * of which is affine isomorphic and weak * -homeomorphic to the state space of L(A). In the case in which A is a JBW * -triple, it is shown that tripotents u and v in A are orthogonal if and only if the corresponding multiplication operators in the unital GM-space L(A) h satisfy 0 D(u, u) + D(v, v) id A , and that u is a pre-associate of v if and only if D(u, u) D(v, v).

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The Norm of a Hermitian Element in a Banach Algebra

Abstract: Abstract.We prove that the norm of a hermitian element in a Banach algebra is equal to the spectral radius of the element.

Cited by 10 publications

References 1 publication

Dissipative operators on Banach spaces

Dissipative operators on Banach spaces

A piece of Victor Katsnelson's mathematical biography

The Banach–Lie algebra of multiplication operators on a JBW∗-triple

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