Spectral radius characterization of commutativity in Banach algebras
Jaroslav Zemánek (1977)
Studia Mathematica
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Jaroslav Zemánek (1977)
Studia Mathematica
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Vladimír Müller (1977)
Commentationes Mathematicae Universitatis Carolinae
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(1994)
Banach Center Publications
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Jaroslav Zemánek (1982)
Banach Center Publications
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James Rovnyak (1982)
Banach Center Publications
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Thomas, Gary M. (1981)
Portugaliae mathematica
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(1990)
Studia Mathematica
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Rachid ElHarti, Mohamed Mabrouk (2015)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Let A and B be two non-unital reduced Banach *-algebras and φ: A → B be a vector space isomorphism. The two following statement holds: If φ is a *-isomorphism, then φ is isometric (with respect to the C*-norms), bipositive and φ maps some approximate identity of A onto an approximate identity of B. Conversely, any two of the later three properties imply that φ is a *-isomorphism. Finally, we show that a unital and self-adjoint spectral isometry between semi-simple Hermitian Banach algebras...
Vlastimil Pták (1982)
Banach Center Publications
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Rudi Brits (2011)
Studia Mathematica
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We extend an example of B. Aupetit, which illustrates spectral discontinuity for operators on an infinite-dimensional separable Hilbert space, to a general spectral discontinuity result in abstract Banach algebras. This can then be used to show that given any Banach algebra, Y, one may adjoin to Y a non-commutative inessential ideal, I, so that in the resulting algebra, A, the following holds: To each x ∈ Y whose spectrum separates the plane there corresponds a perturbation of x, of...