Spectral integration and spectral theory for non-Archimedean Banach spaces.

Ludkovsky, S.; Diarra, B.

Displaying similar documents to “Spectral integration and spectral theory for non-Archimedean Banach spaces.”

Functional calculus for a class of unbounded linear operators on some non-archimedean Banach spaces

Dodzi Attimu, Toka Diagana (2009)

Commentationes Mathematicae Universitatis Carolinae

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This paper is mainly concerned with extensions of the so-called Vishik functional calculus for analytic bounded linear operators to a class of unbounded linear operators on $c_{0}$ . For that, our first task consists of introducing a new class of linear operators denoted $W (c_{0} (J, ω, 𝕂))$ and next we make extensive use of such a new class along with the concept of convergence in the sense of resolvents to construct a functional calculus for a large class of unbounded linear operators.

On discontinuity of the spectral radius in Banach algebras

Vladimír Müller (1977)

Commentationes Mathematicae Universitatis Carolinae

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Properties of the spectral radius in Banach algebras

Jaroslav Zemánek (1982)

Banach Center Publications

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Local spectral radius formula for operators in Banach spaces

Vladimír Müller (1988)

Czechoslovak Mathematical Journal

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Perturbation and spectral discontinuity in Banach algebras

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...