A Banach space operator T ∈ B(X ) is polaroid if points λ ∈ isoσσ(T ) are poles of the resolvent of T . Let σa(T ), σw(T ), σaw(T ), σSF+(T ) and σSF−(T ) denote, respectively, the approximate point, the Weyl, the Weyl essential approximate, the upper semi–Fredholm and lower semi–Fredholm spectrum of T . For A, B and C ∈ B(X ), let MC denote the operator 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.

Let T be an algebraically paranormal operator acting on Hilbert space. We prove : (i) Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T )); (ii) a-Browder’s theorem holds for f(S) for every S ≺ T and f ∈ H(σ(S)); (iii) the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T . Mathematics Subject Classification (2000). Primary 47A10, 4...

The purpose of this study is to determine the fine spectra of the operator for which the corresponding upper and lower triangular matrices A(r, s, t) and B(r, s, t) are on the sequence spaces c and lp, where (0 < p < 1), respectively. Further, we obtain the approximate point spectrum, defect spectrum and compression spectrum on these spaces. Furthermore, we give the graphical representations of...

The operator A r̃, s̃ on sequence space on p is defined A r̃, s̃ x rkxk skxk 1 ∞ k 0, where x xk ∈ p, and r̃ and s̃ are two convergent sequences of nonzero real numbers satisfying certain conditions, where 1 < p < ∞ . The main purpose of this paper is to determine the fine spectrum with respect to the Goldberg’s classification of the operator A r̃, s̃ defined by a double sequential band matrix over the...

Spectrum is a valuable, scarce and finite natural resource that is needed for many different applications, so efficient use of the scarce radio spectrum is important for accommodating the rapid growth of wireless communications. Spectrum auctions are one of the best-known market-based solutions to improve the efficiency of spectrum use. However, Spectrum auctions are fundamentally differen...