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

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Abstract: Let be a bounded operator in a Banach space . Suppose that has the single valued extension property. Given a closed set in the complexes, define to be the set of all in such that there is an analytic function from the complement of to with . is said to have property if is a closed subset of for every .

Let be, again, a bounded operator in a Banach space . Given a real number , define to be the set of all in such that is a bounded function from the nonnegative reals to for all . is said to have property if is a closed subspace of for all .

These two properties are discussed in this paper.

**[1]**Ion Colojoară and Ciprian Foiaş,*Theory of generalized spectral operators*, Gordon and Breach, Science Publishers, New York-London-Paris, 1968. Mathematics and its Applications, Vol. 9. MR**0394282****[2]**Nelson Dunford and Jacob T. Schwartz,*Linear Operators. I. General Theory*, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. MR**0117523****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]**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****[4]**Kôsaku Yosida,*Functional analysis*, Second edition. Die Grundlehren der mathematischen Wissenschaften, Band 123, Springer-Verlag New York Inc., New York, 1968. MR**0239384**

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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