Some remarks on commutative algebras of operators on Banach spaces

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Remarks on Commutative Hilbert Algebras

The paper shows that commutative Hilbert algebras introduced by Y.B. Jun are just J. C.Abbot’s implication algebras.

Linear operators of Banach spaces with range in Lipschitz algebras

In this paper, a complete description concerning linear operators of Banach spaces with range in Lipschitz algebras $lip_al(X)$ is provided. Necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. Finally, a lower bound for the essential norm of such operators is obtained.

K-Theory for Algebras of Operators on Banach Spaces

We prove that, for each pair (m,n) of non-negative integers, there is a Banach space X for which K0(B(X)) ∼= Z m and K1(B(X)) ∼= Z . Along the way we compute the K-groups of all closed ideals of operators contained in the ideal of strictly singular operators, and we derive some results about the existence of splittings of certain short exact sequences.

Banach Algebras of Operators on Locally Convex Spaces