Glasnik Matematicki, Vol. 50, No. 2 (2015), 429-440.

LOCALIZED SVEP AND THE COMPONENTS OF QUASI-FREDHOLM RESOLVENT SET

Qingping Zeng, Huaijie Zhong and Qiaofen Jiang

School of Mathematics and Computer Science, Fujian Normal University, 350007 Fuzhou, P.R. China
e-mail: zhonghuaijie@sina.com
e-mail: bj001_ren@163.com

Abstract.   In this paper, new characterizations of the single valued extension property are given, for a bounded linear operator T acting on a Banach space and its adjoint T^*, at Λ₀ C in the case that Λ₀ I - T is quasi-Fredholm. With the help of a classical perturbation result concerning operators with eventual topological uniform descent, we show the constancy of certain subspace valued mappings on the components of quasi-Fredholm resolvent set. As a consequence, we obtain a classification of these components.

2010 Mathematics Subject Classification.   47A10, 47A11, 47A55.

Key words and phrases.   Single valued extension property, quasi-Fredholm operators, quasi-Fredholm resolvent set.

DOI: 10.3336/gm.50.2.11

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