Extended local spectral properties for a block matrix linear relations thought ER-SVEP
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In the present paper, under some new conditions we prove that the sum of two linear relations has the extended Bishop property in the extended complex plane. Also, we develop and generalize a local spectral theory for block matrix of linear relations. More precisely, this paper considers a necessary and sufficient conditions on the diagonal entries of $2\times2$-block matrix linear relations ensuring that this matrix has extended Bishop's property, extended Dunford's property and extended relatively single-valued extension property.
Abstract
In the present paper, under some new conditions we prove that the sum of two linear relations has the extended Bishop property in the extended complex plane. Also, we develop and generalize a local spectral theory for block matrix of linear relations. More precisely, this paper considers a necessary and sufficient conditions on the diagonal entries of $2\times2$-block matrix linear relations ensuring that this matrix has extended Bishop's property, extended Dunford's property and extended relatively single-valued extension property.