Two types of hyperinvariant subspaces
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- by Robert M. Kauffman PDF
- Proc. Amer. Math. Soc. 39 (1973), 553-558 Request permission
Abstract:
Let $A$ be a bounded operator in a Banach space $B$. Suppose that $A$ has the single valued extension property. Given a closed set $F$ in the complexes, define ${\sigma _A}(F)$ to be the set of all $x$ in $B$ such that there is an analytic function $x(\lambda )$ from the complement of $F$ to $B$ with $(A - \lambda I)x(\lambda ) = x$. $A$ is said to have property $Q$ if ${\sigma _A}(F)$ is a closed subset of $B$ for every $F$. Let $A$ be, again, a bounded operator in a Banach space $B$. Given a real number $b$, define ${S_A}(b)$ to be the set of all $x$ in $B$ such that $\exp ( - ct)\exp (At)x$ is a bounded function from the nonnegative reals to $B$ for all $c > b$. $A$ is said to have property $\operatorname {P}$ if ${S_A}(b)$ is a closed subspace of $B$ for all $b$. These two properties are discussed in this paper.References
- Ion Colojoară and Ciprian Foiaş, Theory of generalized spectral operators, Mathematics and its Applications, Vol. 9, Gordon and Breach Science Publishers, New York-London-Paris, 1968. MR 0394282
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523 (b) —, Linear operators. II. Spectral theory. Selfadjoint operators in Hilbert space, Interscience, New York, 1963. MR 32 #6181. (c) —, Linear operators. III. Spectral operators, Interscience, New York, 1971.
- Peter A. Fillmore, Notes on operator theory, Van Nostrand Reinhold Mathematical Studies, No. 30, Van Nostrand Reinhold Co., New York-London-Melbourne, 1970. MR 0257765
- Kôsaku Yosida, Functional analysis, 2nd ed., Die Grundlehren der mathematischen Wissenschaften, Band 123, Springer-Verlag New York, Inc., New York, 1968. MR 0239384
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 553-558
- MSC: Primary 47A15; Secondary 47B40
- DOI: https://doi.org/10.1090/S0002-9939-1973-0336389-5
- MathSciNet review: 0336389