On the equations X=KXS and AX=XK
Peter Rosenthal (1982)
Banach Center Publications
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Displaying similar documents to “Two characterizations of automorphisms on B(X)”
On the equations X=KXS and AX=XK
A generalization of peripherally-multiplicative surjections between standard operator algebras
Takeshi Miura, Dai Honma (2009)
Open Mathematics
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Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum σπ (T) of T is defined by σπ (T) = z ∈ σ(T): |z| = maxw∈σ(T) |w|. If surjective (not necessarily linear nor continuous) maps φ, ϕ: A → B satisfy σπ (φ(S)ϕ(T)) = σπ (ST) for all S; T ∈ A, then φ and ϕ are either of the form φ(T) = A 1 TA 2 −1 and ϕ(T) = A 2 TA 1 −1 for some bijective bounded linear operators A 1; A 2 of X onto Y, or of the form φ(T) = B 1 T*B 2 −1 and ϕ(T) = B 2 T*B...
On joint spectra of commuting families of operators
W. Żelazko, Z. Słodkowski (1974)
Studia Mathematica
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The splitting spectrum differs from the Taylor spectrum
V. Müller (1997)
Studia Mathematica
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We construct a pair of commuting Banach space operators for which the splitting spectrum is different from the Taylor spectrum.
On the axiomatic theory of spectrum
V. Kordula, V. Müller (1996)
Studia Mathematica
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There are a number of spectra studied in the literature which do not fit into the axiomatic theory of Żelazko. This paper is an attempt to give an axiomatic theory for these spectra, which, apart from the usual types of spectra, like one-sided, approximate point or essential spectra, include also the local spectra, the Browder spectrum and various versions of the Apostol spectrum (studied under various names, e.g. regular, semiregular or essentially semiregular).
On joint spectra of operators on a Banach space isomorphic to its square
Andrzej Sołtysiak (1989)
Colloquium Mathematicae
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Diagonals of Self-adjoint Operators with Finite Spectrum
Marcin Bownik, John Jasper (2015)
Bulletin of the Polish Academy of Sciences. Mathematics
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Given a finite set X⊆ ℝ we characterize the diagonals of self-adjoint operators with spectrum X. Our result extends the Schur-Horn theorem from a finite-dimensional setting to an infinite-dimensional Hilbert space analogous to Kadison's theorem for orthogonal projections (2002) and the second author's result for operators with three-point spectrum (2013).
Identity of Taylor's joint spectrum and Dash's joint spectrum
Muneo Chō, Makoto Takaguchi (1981)
Studia Mathematica
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On operators with the same spectrum
Gh. Constantin (1975)
Matematički Vesnik
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The beginning of the spectral theory of Nevanlinna's mapping from topological space to endomorphisms algebra of Banach space and its applications.
Ragimov, Misir B. (2003)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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The boundary of Taylor's joint spectrum for two commuting Banach space operators
Volker Wróbel (1986)
Studia Mathematica
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On rank one and finite elements of Banach algebras
T. Mouton, H. Raubenheimer (1993)
Studia Mathematica
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We give a spectral characterisation of rank one elements and of the socle of a semisimple Banach algebra.
The Słodkowski spectra and higher Shilov boundaries
Vladimír Müller (1993)
Studia Mathematica
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We investigate relations between the spectra defined by Słodkowski [14] and higher Shilov boundaries of the Taylor spectrum. The results generalize the well-known relation between the approximate point spectrum and the usual Shilov boundary.