Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 6 (2011), 137 -- 159


Simona Macovei

Abstract. Having as start point the classic definitions of resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the resolvent set and spectrum of a family of linear bounded operators on a Banach space. In addition, we present some results which adapt to asymptotic case the classic results.

2010 Mathematics Subject Classification: 47-01; 47A10.
Keywords: spectrum; resolvent set; asymptotic equivalence; asymptotic quasinilpotent equivalence.

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Simona Macovei
University of Bucharest,
Str. Academiei nr.14, Bucureşti,