Displaying similar documents to “Browder Riesz-Schauder theory for polynomially finite rank linear relations”

Trace and determinant in Banach algebras

Bernard Aupetit, H. Mouton (1996)

Studia Mathematica

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We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.

Plus-Minus Property as a Generalization of the Daugavet Property

Shepelska, Varvara (2010)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 46B20. Secondary 47A99, 46B42. It was shown in [2] that the most natural equalities valid for every rank-one operator T in real Banach spaces lead either to the Daugavet equation ||I+T|| = 1 + ||T|| or to the equation ||I − T|| = ||I+T||. We study if the spaces where the latter condition is satisfied for every finite-rank operator inherit the properties of Daugavet spaces.

Finite spectra and quasinilpotent equivalence in Banach algebras

Rudi M. Brits, Heinrich Raubenheimer (2012)

Czechoslovak Mathematical Journal

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This paper further investigates the implications of quasinilpotent equivalence for (pairs of) elements belonging to the socle of a semisimple Banach algebra. Specifically, not only does quasinilpotent equivalence of two socle elements imply spectral equality, but also the trace, determinant and spectral multiplicities of the elements must agree. It is hence shown that quasinilpotent equivalence is established by a weaker formula (than that of the spectral semidistance). More generally,...

Banach spaces which embed into their dual

Valerio Capraro, Stefano Rossi (2011)

Colloquium Mathematicae

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We use Birkhoff-James' orthogonality in Banach spaces to provide new conditions for the converse of the classical Riesz representation theorem.

Rank, trace and determinant in Banach algebras: generalized Frobenius and Sylvester theorems

Gareth Braatvedt, Rudolf Brits, Francois Schulz (2015)

Studia Mathematica

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As a follow-up to a paper of Aupetit and Mouton (1996), we consider the spectral definitions of rank, trace and determinant applied to elements in a general Banach algebra. We prove a generalization of Sylvester's Determinant Theorem to Banach algebras and thereafter a generalization of the Frobenius inequality.

Rank and the Drazin inverse in Banach algebras

R. M. Brits, L. Lindeboom, H. Raubenheimer (2006)

Studia Mathematica

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Let A be an arbitrary, unital and semisimple Banach algebra with nonzero socle. We investigate the relationship between the spectral rank (defined by B. Aupetit and H. Mouton) and the Drazin index for elements belonging to the socle of A. In particular, we show that the results for the finite-dimensional case can be extended to the (infinite-dimensional) socle of A.

On the Kleinecke-Shirokov Theorem for families of derivations

Victor S. Shulman, Yuriĭ V. Turovskii (2002)

Studia Mathematica

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It is proved that Riesz elements in the intersection of the kernel and the closure of the image of a family of derivations on a Banach algebra are quasinilpotent. Some related results are obtained.