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ArticleOriginal scientific text

Title

On the joint spectral radii of commuting Banach algebra elements

Authors 1

Affiliations

  1. Institute of Mathematics, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland

Abstract

Some inequalities are proved between the geometric joint spectral radius (cf. [3]) and the joint spectral radius as defined in [7] of finite commuting families of Banach algebra elements.

Bibliography

  1. M. A. Berger and Y. Wang, Bounded semigroups of matrices, Linear Algebra Appl. 166 (1992), 21-27.
  2. F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin 1973.
  3. M. Chō and W. Żelazko, On geometric spectral radius of commuting n-tuples of operators, Hokkaido Math. J. 21 (1992), 251-258.
  4. R. E. Harte, Spectral mapping theorems, Proc. Roy. Irish Acad. Sect. A 72 (1972), 89-107.
  5. A. Ya. Khelemskiĭ, Banach and Polynormed Algebras: General Theory, Representations, Homology, Nauka, Moscow 1989 (in Russian).
  6. V. Müller and A. Sołtysiak, Spectral radius formula for commuting Hilbert space operators, Studia Math. 103 (1992), 329-333.
  7. G.-C. Rota and W. G. Strang, A note on the joint spectral radius, Indag. Math. 22 (1960), 379-381.
  8. A. Sołtysiak, On a certain class of subspectra, Comment. Math. Univ. Carolinae 32 (1991), 715-721.
Studia Mathematica
1993/105/1
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Pages:
93-99
Main language of publication
English
Received
1992-08-31
Accepted
1992-10-23
Published
1993
Exact and natural sciences