Generalized positive linear functionals on a Banach algebra with an involution

Banach Algebra of Bounded Functionals

Let V be a non empty additive loop structure and let V1 be a subset of V . We say that V1 has inverse if and only if: (Def. 1) For every element v of V such that v ∈ V1 holds −v ∈ V1. Let V be a non empty additive loop structure and let V1 be a subset of V . We say that V1 is additively-closed if and only if: (Def. 2) V1 is add closed and has inverse. Let V be a non empty additive loop structur...

Linear Functionals on Certain Banach Spaces

Banach Algebra of Bounded Complex-Valued Functionals

The notation and terminology used in this paper are introduced in the following articles: [2], [16], [9], [14], [7], [8], [3], [18], [17], [4], [19], [5], [15], [1], [20], [12], [11], [10], [21], [13], and [6]. Let V be a complex algebra. A complex algebra is called a complex subalgebra of V if it satisfies the conditions (Def. 1). (Def. 1)(i) The carrier of it ⊆ the carrier of V , (ii) the add...

A Remark on Continuity of Positive Linear Functionals on Separable Banach *-Algebras

Using a variation of the Murphy-Varopoulos Theorem, we give a new proof of the following R. J. Loy Theorem: Let A be a separable Banach ∗-algebra with center Z such that ZA has at most countable codimension, then every positive linear functional on A is continuous.

Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra

In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...