We offer a new definition of $varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $varepsilon$-orthogonality in an arbitrary  $C^ast$-algebra $mathcal{A}$, as a Hilbert $C^ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.

Abstract We initiate the study of computable presentations real and complex C*-algebras under program effective metric structure theory. With group situation as a model, we develop corresponding notions recursive word problems for C*-algebras, show some analogous results hold in this setting. Famously, every finitely generated with presentation is computably categorical, but provide counterexam...

A ternary [n, k] code C is a k-dimensional vector subspace of Fn3 , where F3 denotes the finite field of order 3. The weight wt(x) of a vector x is the number of non-zero components of x. The minimum non-zero weight of all codewords in C is called the minimum weight of C. A ternary [n, k, d] code is a ternary [n, k] code with minimum weight d. Throughout this note, we denote the minimum weight ...

This is the final one in the series of papers where we introduce and study the C∗-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated C∗-algebras are simple and purely infinite. Using this result, we give one method to construct all Kirchberg algebras as C∗-algebras associated with topological graphs. 0. Introduc...

Suppose $pi:mathcal{A}rightarrow mathcal{B}$ is a surjective unital $ast$-homomorphism between C*-algebras $mathcal{A}$ and $mathcal{B}$, and $0leq aleq1$ with $ain  mathcal{A}$. We give a sufficient condition that ensures there is a proection $pin mathcal{A}$ such that $pi left( pright) =pi left( aright) $. An easy consequence is a result of [L. G. Brown and G. k. Pedersen, C*-algebras of real...

In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$  associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $  C^* $-algebra  $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the ...

We study C?-irreducibility of inclusions reduced twisted group C?-algebras and C?-algebras. characterize in the case an inclusion arising from a normal subgroup, exhibit many new examples C?-irreducible inclusions.

We introduce and study continuous fields of JB-algebras (which are real non-associate analogues of C*-algebras). In particular, we show that for the universal enveloping C*-algebra C∗ u (B) for the JB-algebra B defined by a continuous field of JB-algebras At, t ∈ T, on a locally compact space T there exists a decomposition of C∗ u (B) into a continuous field of C*-algebras C∗ u (At), t ∈ T, on ...