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A spectral mapping theorem for the Weyl spectrum

Published online by Cambridge University Press:  18 May 2009

Woo Young Lee  and
Sang Hoon Lee
Woo Young Lee
Affiliation:
Department of Mathematics, Sung Kyun Kwan University, Suwon 440-746, Korea, E-mail address: wylee@yurim.skku.ac.kr
Sang Hoon Lee
Affiliation:
Department of Mathematics, Sung Kyun Kwan University, Suwon 440-746, Korea, E-mail address: wylee@yurim.skku.ac.kr
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Suppose H is a Hilbert space and write ℒ(H) for the set of all bounded linear operators on H. If T ∈ ℒ(H) we write σ(T) for the spectrum of T; π0(T) for the set of eigenvalues of T; and π00(T) for the isolated points of σ(T) that are eigenvalues of finite multiplicity. If K is a subset of C, we write iso K for the set of isolated points of K. An operator T ∈ ℒ(H) is said to be Fredholm if both T−1(0) and T(H)⊥ are finite dimensional. The index of a Fredholm operator T, denoted by index(T), is defined by

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 1 , January 1996 , pp. 61 - 64
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

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