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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On locally linearly dependent operators
and derivations


Authors: Matej Bresar and Peter Semrl
Journal: Trans. Amer. Math. Soc. 351 (1999), 1257-1275
MSC (1991): Primary 15A04, 16W25, 47B47; Secondary 46H05, 47B48
MathSciNet review: 1621729
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Abstract | References | Similar Articles | Additional Information

Abstract: The first section of the paper deals with linear operators $T_i:U\longrightarrow V$, $i = 1,\ldots,n$, where $U$ and $V$ are vector spaces over an infinite field, such that for every $u \in U$, the vectors $T_1 u,\ldots,T_n u$ are linearly dependent modulo a fixed finite dimensional subspace of $V$. In the second section, outer derivations of dense algebras of linear operators are discussed. The results of the first two sections of the paper are applied in the last section, where commuting pairs of continuous derivations $d,g$ of a Banach algebra ${\cal A}$ such that $(dg)(x)$ is quasi-nilpotent for every $x \in {\cal A}$ are characterized.


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Additional Information

Matej Bresar
Affiliation: Department of Mathematics, University of Maribor PF, Koroška 160\ 2000 Maribor, Slovenia
Email: bresar@uni-mb.sl

Peter Semrl
Affiliation: Department of Mathematics, University of Maribor SF, Smetanova 17\ 2000 Maribor, Slovenia
Email: peter.semrl@uni-mb.sl

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02370-3
PII: S 0002-9947(99)02370-3
Received by editor(s): February 12, 1997
Additional Notes: The authors were supported in part by the Ministry of Science of Slovenia.
Article copyright: © Copyright 1999 American Mathematical Society