a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...

1. Topological Vector Spaces 1 1.1. The Krein-Milman theorem 7 2. Banach Algebras 11 2.1. Commutative Banach algebras 14 2.2. ∗–Algebras (over complexes) 17 2.3. Problems on Banach algebras 20 3. The Spectral Theorem 21 3.1. Problems on the Spectral Theorem (Multiplication Operator Form) 26 3.2. Integration with respect to a Projection Valued Measure 27 3.3. The Functional Calculus 34 4. Unboun...

The Banach frame for a Banach space  can reconstruct each vector in  by the pre-frame operator or the reconstruction operator. The Banach Λ-frame for operator spaces was introduced by Kaushik, Vashisht and Khattar [Reconstruction Property and Frames in Banach Spaces, Palestine Journal of Mathematics, 3(1), 2014, 11-26]. In this paper we give necessary and sufficient conditions for the existen...

In the group of (continuous) Jordan automorphisms, with the uniform topology, on a semisimple Banach algebra, we show that the connected component of the identity consists of automorphisms. P. Civin and B. Yood have shown that a Jordan homomorphism (that is, a homomorphism that preserves the product xoy = | (xy+yx)) from a Banach algebra onto a semisimple Banach algebra is continuous provided t...

1. Topological Vector Spaces 1 1.1. The Krein-Milman theorem 7 2. Banach Algebras 11 2.1. Commutative Banach algebras 14 2.2. ∗–Algebras (over complexes) 17 2.3. Problems on Banach algebras 20 3. The Spectral Theorem 21 3.1. Problems on the Spectral Theorem (Multiplication Operator Form) 26 3.2. Integration with respect to a Projection Valued Measure 27 3.3. The Functional Calculus 34 4. Unboun...

For a family of operator inclusions with convex closed-valued right-hand sides in Banach spaces, the existence of solutions is obtained by chieey using Ky Fan's xed point principle. The main result of the paper improves Theorem 1 in 16] as well as Theorem 2.2 of 3]. Some meaningful concrete cases are also presented and discussed. KEY WORDS: operator inclusions in Banach spaces, Ky Fan's xed poi...

We prove a version of Hahn-Banach Theorem. and 1] provide the notation and terminology for this paper. The following propositions are true: (1) For all sets x, y and for every function f such that h hx; yi i 2 f holds y 2 rng f: (2) For every set X and for all functions f, g such that X dom f and f g holds fX = gX: (3) For every non empty set A and for every set b such that A 6 = fbg there exis...

Several results are proved concerning representations of multiplier algebras that arise as extensions of representations of underlying Banach algebras. These results are then used to rederive Kisyński’s generalisation of the Hille–Yosida theorem and to establish two generalisations of the Trotter–Kato theorem, one of which, involving Banach bundles, is abstract and the other is classical in cha...

In fact, if X is any vector space on which the primitive Banach algebra A acts faithfully and irreducibly, then X can be converted in a Banach space in such a way that the requirements in Theorem 0 are satisfied and even the inclusion A9BL(X ) is contractive. Roughly speaking, the aim of this paper is to prove the appropriate Jordan variant of Theorem 0. The notion of primitiveness for Jordan a...