A wide new class of subsets a Banach space X named coarse p-limited sets ( $$ 1\le p < \infty ) is introduced by considering weak* p-summable sequences in $$X'$$ instead null sequences. We study its basic properties and compare it with the compact weakly sets. Results concerning relationship operators are obtained.

We propose and analyze a new spectral collocation method to solve eigenvalue problems of compact integral operators, particularly, piecewise smooth operator kernels and weakly singular operator kernels of the form 1 |t−s|μ , 0 < μ < 1. We prove that the convergence rate of eigenvalue approximation depends upon the smoothness of the corresponding eigenfunctions for piecewise smooth kernels. On t...

We introduce and study a new topology on trees, that we call the countably coarse wedge topology. Such is strictly finer than it turns every chain complete, rooted tree into Fréchet–Urysohn, compact topological space. show rôle of such in theory weakly Corson Valdivia compacta. In particular, give first example space T whose closed subspace Valdivia, yet not Corson. This answers question due to...

The Kuznetsov–Index of a modal logic is the least cardinal μ such that any consistent formula has a Kripke–model of size ≤ μ if it has a Kripke–model at all. The Kuznetsov–Spectrum is the set of all Kuznetsov–Indices of modal logics with countably many operators. It has been shown by Thomason that there are tense logics with Kuznetsov–Index iω+ω. Futhermore, Chagrov has constructed an extension...

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

the aim of this paper is to establish random coincidence point results for weakly increasing random operators in the setting of ordered metric spaces by using generalized altering distance functions. our results present random versions and extensions of some well-known results in the current literature.

The weakly compact reflection principle Reflwcpκq states that κ is a weakly compact cardinal and every weakly compact subset of κ has a weakly compact proper initial segment. The weakly compact reflection principle at κ implies that κ is an ω-weakly compact cardinal. In this article we show that the weakly compact reflection principle does not imply that κ is pω ` 1qweakly compact. Moreover, we...

Read produced the first example of a Banach space ER such that the associated Banach algebra B(ER) of bounded operators admits a discontinuous derivation (J. London Math. Soc. 1989). We generalize the main theorem about B(ER) from which Read deduced this conclusion, as well as the key technical step in his proof, by constructing a strongly split-exact sequence {0} −→ W (ER) −→ B(ER) −→ ←− l2(N)...

in this paper‎, ‎we show the stability of gustafson‎, ‎weidmann‎, ‎kato‎, ‎wolf‎, ‎schechter and browder essential spectrum of bounded linear operators on banach spaces which remain invariant under additive perturbations‎ ‎belonging to a broad classes of operators $u$ such $gamma(u^m)