Representations ofH ?(G) and invariant subspaces

Eschmeier, Jörg

doi:10.1007/bf01459732

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Preliminaries1

Invariant Subspaces1

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1995

2010

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Cited by 8 publications

(4 citation statements)

References 18 publications

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“…This paper constitutes part of the author's Ph.D. thesis written at Texas A&M University under the direction of Carl Pearcy. The referee has kindly pointed out that Jörg Eschmeier obtained a similar result in [10].…”

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confidence: 75%

On polynomially bounded operators with rich spectrum

Gadidov¹

1995

Proc. Amer. Math. Soc.

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confidence: 75%

On polynomially bounded operators with rich spectrum

Gadidov¹

1995

Proc. Amer. Math. Soc.

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“…The extension to arbitrary Banach spaces is easy, following the lines in the above mentioned proofs. The following theorem, obtained in [3] and [13], is the basic tool in proving our main result. …”

Section: Preliminariesmentioning

confidence: 96%

K-spectral sets and invariant subspaces

Prunaru

1996

Integr equ oper theory

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In this paper we show that given any Banach space operator T whose spectrum is a k-spectral set, its adjoint T* has a nontrivial invariant subspace. INTRODUCTIONThe dual algebras techniques, initiated by S. Brown in [5], have been very successful in dealing with Hilbert space operators. Extending these techniques to the setting of Banach space operators is a rather difficult task. However, in recent years, several important results in this direction have been obtained (see [2], [31, [111, [121, [131 and [14]) and there are still many open problems in this area.In this note we show that some of the results relating k-spectral sets and invariant subspaces for operators on Hilbert spaces (see [1], [4], [17] and [18]) can be extended to operators on arbitrary Banach spaces.

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“…Suppose that T also satisfies the condition that jjT n ujj-0 for all uAX : It is a folklore result that then all the functionals x#x Ã where xAX and x Ã AX Ã can be represented by absolutely continuous measures, and so these functionals are of the [A2,E,KO,Sz]. Usually, such results are proved by defining the H N calculus for T (by means of radial limits) and by showing that this functional calculus is ðw Ã ; SOTÞ continuous.…”

Section: Invariant Subspacesmentioning

confidence: 99%