we define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital banach algebra a and show that the δ-approximate spectrum σ_δ (a) of a is compact. the relation between the δ-approximate spectrum and the usual spectrum is investigated. also an analogue of the classical gleason-kahane-zelazko theorem is established: for each ε>0, there is δ>0 such that if ϕ is...

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

Fine spectra of various matrix operators on different sequence spaces have been examined by several authors. Recently, some authors have determined the approximate point spectrum, the defect spectrum and the compression spectrum of various matrix operators on different sequence spaces. Here in this article we have determined the spectrum and fine spectrum of the lower triangular matrix B(r,0,s)...

Fine spectra of various matrix operators on different sequence spaces have been examined by several authors. Recently, some authors have determined the approximate point spectrum, the defect spectrum and the compression spectrum of various matrix operators on different sequence spaces. Here in this article we have determined the spectrum and fine spectrum of the lower triangular matrix   , , ...

in this paper, we prove some approximate fixed point results for proximinal valued $beta$-contractive multifunctions on metric spaces. we show that our results generalize some old fixed point results in the literature.

The spectral mapping theorem for joint approximate point spectrum is proved when A is an «-tuple of commuting operators on a Banach space and ƒ is any w-tuple of rational functions for which f (A) is defined. The purpose of the paper is to show how properties of parts of the joint spectrum can be obtained by use of spaces of sequences of vectors. The method (first used for general Banach spaces...