We represent every normal-valued GMV-algebra as a GMV-algebra of real-valued functions; we also describe the universal MV-algebras and universal normal-valued GMV-algebras with a prescribed set of components.

We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued (∈,∈ ∨ q)-fuzzy filters of pseudo BL-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these ge...

The aim of this work is to study a class of non-archimedean valued measures on MV-algebras. We call them hyperreal states and their definition naturally arise from (the uniform version of) Di Nola representation theorem for MV-algebras (cf [5, 6]): for any MV-algebra A = (A,⊕,¬,>,⊥) there exists a ultrafilter U on the cardinality of A such that A embeds into (∗[0, 1]U) Spec(A) (where as usual S...

In a recent work, thanks to the use of Cliiord algebras and designants, we have shown that Wynn's vector "-algorithm can be written as a ratio of two designants. The present work, according to these new results, has the aim of 1. Finding easily and diierently the results of some authors in this scope, particularly those of Wynn, D.E. Roberts and P.R. Graves-Morris. 2. Computing explicitly the e...

Abstract In this article, without requiring solidness of the underlying cone, a kind new convergence for sequences in cone b b -metric spaces over Banach algebras and completeness such spaces, namely, wrtn-completeness, are introduced. Under condition that wrtn-complete cones normal, we establish common fixed point the...

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-al...

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...

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...

We present several embedding results for 3-graded Lie algebras and KKT algebras that are generated by two homogeneous elements of degrees 1 and −1. We also propose the canonical kernel function for a “universal Bergman kernel” which extends the usual Bergman kernel on a bounded symmetric domain to a group-valued function or, in terms of formal series, to an element in the formal completion of t...