Abstract
Starting from the classic definitions of resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the local resolvent set and local spectrum, the local spectral space and the single-valued extension property of a family of linear bounded operators on a Banach space. Keeping the analogy with the classic case, we extend some of the known results from the case of a linear bounded operator to the case of a family of linear bounded operators on a Banach space.
Citation
Simona Macovei. "Local Spectrum of a Family of Operators." Ann. Funct. Anal. 4 (2) 131 - 143, 2013. https://doi.org/10.15352/afa/1399899531
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