On the equations X=KXS and AX=XK
Peter Rosenthal (1982)
Banach Center Publications
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Peter Rosenthal (1982)
Banach Center Publications
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Kovacs, Istvan (2005)
Abstract and Applied Analysis
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Aaron Luttman, Scott Lambert (2008)
Open Mathematics
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In recent years much work has been done analyzing maps, not assumed to be linear, between uniform algebras that preserve the norm, spectrum, or subsets of the spectra of algebra elements, and it is shown that such maps must be linear and/or multiplicative. Letting A and B be uniform algebras on compact Hausdorff spaces X and Y, respectively, it is shown here that if λ ∈ ℂ / 0 and T: A → B is a surjective map, not assumed to be linear, satisfying then T is an ℝ-linear isometry and there...
Ulrich Groh (1981)
Mathematische Zeitschrift
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Peter Šemrl (1993)
Studia Mathematica
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Let X be an infinite-dimensional Banach space, and let ϕ be a surjective linear map on B(X) with ϕ(I) = I. If ϕ preserves injective operators in both directions then ϕ is an automorphism of the algebra B(X). If X is a Hilbert space, then ϕ is an automorphism of B(X) if and only if it preserves surjective operators in both directions.
Andrzej Sołtysiak (1989)
Colloquium Mathematicae
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Linus Carlsson, Urban Cegrell, Anders Fällström (2007)
Annales Polonici Mathematici
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We study the spectrum of certain Banach algebras of holomorphic functions defined on a domain Ω where ∂̅-problems with certain estimates can be solved. We show that the projection of the spectrum onto ℂⁿ equals Ω̅ and that the fibers over Ω are trivial. This is used to solve a corona problem in the special case where all but one generator are continuous up to the boundary.
W. Żelazko (1979)
Studia Mathematica
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W. Żelazko, Z. Słodkowski (1974)
Studia Mathematica
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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).
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.
Derek Kitson (2009)
Studia Mathematica
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We extend the notion of ascent and descent for an operator acting on a vector space to sets of operators. If the ascent and descent of a set are both finite then they must be equal and give rise to a canonical decomposition of the space. Algebras of operators, unions of sets and closures of sets are treated. As an application we construct a Browder joint spectrum for commuting tuples of bounded operators which is compact-valued and has the projection property.
Kulkarni, S.H., Sukumar, D. (2005)
International Journal of Mathematics and Mathematical Sciences
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Volker Wróbel (1986)
Studia Mathematica
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