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On generalized a-Browder's theorem

Pietro Aiena, T. Len Miller (2007)

Studia Mathematica

We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H₀(λI - T) as λ belongs to certain sets of ℂ. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators.

On generalized derivations in Banach algebras

Nadia Boudi, Said Ouchrif (2009)

Studia Mathematica

We study generalized derivations G defined on a complex Banach algebra A such that the spectrum σ(Gx) is finite for all x ∈ A. In particular, we show that if A is unital and semisimple, then G is inner and implemented by elements of the socle of A.

On generalized inverses in C*-algebras

Robin Harte, Mostafa Mbekhta (1992)

Studia Mathematica

We investigate when a C*-algebra element generates a closed ideal, and discuss Moore-Penrose and commuting generalized inverses.

On generalized property (v) for bounded linear operators

J. Sanabria, C. Carpintero, E. Rosas, O. García (2012)

Studia Mathematica

An operator T acting on a Banach space X has property (gw) if σ a ( T ) σ S B F ¯ ( T ) = E ( T ) , where σ a ( T ) is the approximate point spectrum of T, σ S B F ¯ ( T ) is the upper semi-B-Weyl spectrum of T and E(T) is the set of all isolated eigenvalues of T. We introduce and study two new spectral properties (v) and (gv) in connection with Weyl type theorems. Among other results, we show that T satisfies (gv) if and only if T satisfies (gw) and σ ( T ) = σ a ( T ) .

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