Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 22 Issue 1
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- Pages.23-29
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- 1985
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
SPECTRA OF THE IMAGES UNDER THE FAITHFUL $^*$ -REPRESENTATION OF L(H) ON K
Abstract
Let H be an arbitrary complex Hilbert space. We constructed an extension K of H by means of weakly convergent sequences in H and the Banach limit. Let .phi. be the faithful *-representation of L(H) on K. In this note, we investigated the relations between spectra of T in L(H) and .phi.(T) in L(K) and we obtained the following results: 1) If T is a compact operator on H, then .phi.(T) is also a compact operator on K (Proposition 6), 2) .sigma.
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