Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the multiplicities of the powers of a Banach space operator


Author: Domingo A. Herrero
Journal: Proc. Amer. Math. Soc. 94 (1985), 239-243
MSC: Primary 47A99; Secondary 47B10
MathSciNet review: 784171
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The multiplicities of the powers of a bounded linear operator $ T$, acting on a complex separable infinite-dimensional Banach space $ \mathfrak{X}$, satisfy the inequalities

$\displaystyle ( * * )\qquad \mu ({T^n}) \leqslant \mu ({T^{hn}}) \leqslant h\mu ({T^n})\quad {\text{for}}\;{\text{all}}\;h,n \geqslant 1.$

Nothing else can be said, in general, because simple examples show that for each sequence $ \{ {\mu _n}\} _{n = 1}^\infty $, satisfying the inequalities $ ( * * )$, there exists $ T$ acting on $ \mathfrak{X}$ such that $ \mu ({T^n}) = {\mu _n}$ for all $ n \geqslant 1$.

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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A99, 47B10

Retrieve articles in all journals with MSC: 47A99, 47B10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0784171-5
PII: S 0002-9939(1985)0784171-5
Keywords: Multiplicity of an operator, powers
Article copyright: © Copyright 1985 American Mathematical Society