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Strongly analytic spaces in spectral decomposition

Published online by Cambridge University Press:  18 May 2009

Ridgley Lange  and
Shengwang Wang
Ridgley Lange
Affiliation:
Department of Mathematics, Central Michigan University, Mount Pleasant, Michigan 48859, U.S.A.
Shengwang Wang
Affiliation:
Department of Mathematics, Central Michigan University, Mount Pleasant, Michigan 48859, U.S.A.
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It is now well-known that decomposable operators have a rich structure theory; in particular, an operator is decomposable iff its adjoint is [3]. There are many other criteria for decomposability [8], [9]. In Theorem 2.2 of this paper (see below) we give several new ones. Some of these (e.g. (ii), (iii)) are “relaxations” of conditions given in [7] and [8]. Assertion (vi) is a version of a result in [10]. Characterizations (iv)and (v) are novel in two respects. For instance, (v) states that an operator Tcan be “patched” together into a decomposable operator if it has an invariant subspace Y such that T | Y and the coinduced operator T | Y are both decomposable. Secondly, in this way the strongly analytic subspace appears in the theory of spectral decomposition.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 3 , September 1988 , pp. 249 - 257
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

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