Pseudo-B-Fredholm operators, poles of the resolvent and mean convergence in the calkin algebra
Keyword(s):
We define here a pseudo B-Fredholm operator as an operator such that 0 is isolated in its essential spectrum, then we prove that an operator T is pseudo-B-Fredholm if and only if T = R + F where R is a Riesz operator and F is a B-Fredholm operator such that the commutator [R,F] is compact. Moreover, we prove that 0 is a pole of the resolvent of an operator T in the Calkin algebra if and only if T = K + F, where K is a power compact operator and F is a B-Fredholm operator, such that the commutator [K,F] is compact. As an application, we characterize the mean convergence in the Calkin algebra.
2006 ◽
Vol 11
(3)
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pp. 331-346
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1946 ◽
Vol 32
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pp. 8-10
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1949 ◽
Vol 16
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pp. 189-191
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1975 ◽
Vol 26
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pp. 153-162
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2010 ◽
Vol 62
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pp. 943-960
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1993 ◽
Vol 54
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pp. 287-303
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1972 ◽
Vol 23
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pp. 365-372
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