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.

One-dimensional particle states are constructed according to orthogonality conditions, without requiring boundary conditions. Free particle states are constructed using Dirac’s delta function orthogonality conditions. The states (doublets) depend on two quantum numbers: energy and parity (”+” or ”-”). With the aid of projection operators the particles are confined to a constrained region, in a ...

An orthogonality space is a set equipped with symmetric and irreflexive binary relation. We consider spaces the additional property that any collection of mutually orthogonal elements gives rise to structure Boolean algebra. Together maps preserve substructures, we are led category NOS normal spaces. Moreover, an finite rank called linear if for two distinct e f there third one g such exactly p...

Let $M$ and $N$ be Archimedean vector lattices. We introduce orthogonally additive band operators inverse from to examine their properties. investigate the relationship between disjointness preserving show that under some assumptions on lattices or $N$, these two classes are same. By using this relation, we if ${\mu }$ is a bijective operator (resp. operator) into then }^{-1}$:$N$${\rightarrow}...

We examine some recent results of Bownik on density and connectivity of the wavelet frames. We use orthogonality (strong disjointness) properties of frame and Bessel sequences, and also properties of Bessel multipliers (operators that map wavelet Bessel functions to wavelet Bessel functions). In addition we obtain an asymptotically tight approximation result for wavelet frames.

Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/repns/notes 2014-15/01 finite abelian.pdf] 1. Simultaneous eigenvectors for finite abelian groups 2. Cancellation lemma, orthogonality of distinct characters 3. Representations of finite abelian groups 4. Fourier expansions on finite abelian groups 5. Appendix: spectral theor...

We characterize linear operators preserving zero-restrictions on entire functions in weighted Bargmann–Fock spaces. This extends the characterization of linear operators on polynomials preserving stability (due to Borcea and the author) to the realm of entire functions, and translates into an optimal, albeit formal, Lee–Yang theorem.

In this paper, we investigate the properties of join preserving maps in complete residuated lattices. We define join approximation operators as a generalization of fuzzy rough sets in complete residuated lattices. Moreover, we investigate the relations between join preserving operators and Alexandrov fuzzy topologies. We give their examples. AMS Subject Classification: 03E72, 03G10, 06A15, 06F07