Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Two types of hyperinvariant subspaces


Author: Robert M. Kauffman
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] I. Colojoara and C. Foias, Theory of generalized spectral operators, Math. and Appl., vol. 9, Gordon and Breach, New York, 1968. MR 0394282 (52:15085)
  • [2] (a) N. Dunford and J. T. Schwartz, Linear operators. I. General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • 1. (b) -, Linear operators. II. Spectral theory. Selfadjoint operators in Hilbert space, Interscience, New York, 1963. MR 32 #6181.
  • 2. (c) -, Linear operators. III. Spectral operators, Interscience, New York, 1971.
  • [3] P. Fillmore, Notes on operator theory, Math Studies, no. 30, Van Nostrand Reinhold, New York, 1970. MR 41 #2414. MR 0257765 (41:2414)
  • [4] K. Yosida, Functional analysis, 2nd ed., Die Grundlehren der math. Wissenschaften, Band 123, Springer-Verlag, New York, 1968. MR 39 #741. MR 0239384 (39:741)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A15, 47B40

Retrieve articles in all journals with MSC: 47A15, 47B40


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0336389-5
Keywords: Hyperinvariant subspace, single valued extension property, spectral operator, quasinilpotent operator, hyponormal operator
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society