Bounded, conservative, linear operators and the maximal group. II

Authors:
E. P. Kelly and D. A. Hogan

Journal:
Proc. Amer. Math. Soc. **38** (1973), 298-302

MSC:
Primary 46L20

MathSciNet review:
0313832

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Abstract: Let denote an infinite dimensional Banach space over the complex field, the bounded linear operators on and a closed subspace of . An element of is called a conservative operator. Some sufficient conditions for to be in the boundary, , of the maximal group, , of invertible elements are determined. For example, if , is such that (i) is the topological direct sum of and , (ii) is an automorphism on , then . Also, the complement of the closure of is discussed. This is an extension of another paper by the same authors [**6**].

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DOI:
https://doi.org/10.1090/S0002-9939-1973-0313832-9

Keywords:
Banach algebra,
maximal group,
boundary of maximal group,
bounded operator,
conservative operator,
projection,
quasi-compact operator

Article copyright:
© Copyright 1973
American Mathematical Society