Norm equality for a basic elementary operator

Norm for Sums of Two Basic Elementary Operators

An Operator Equality Involving a Continuous Field of Operators and Its Norm Inequalities

Let A be a C *-algebra, T be a locally compact Hausdorff space equipped with a probability measure P and let (A t) t∈T be a continuous field of operators in A such that the function t → A t is norm continuous on T and the function t → A t is integrable. Then the following equality including Bouchner integrals holds T A t − T A s dP 2 dP = T |A t | 2 dP − T A t dP 2. (0.1) This equality is relat...

On Elementary Equivalence for Equality-free Logic

This paper is a contribution to the study of equality-free logic, that is, first-order logic without equality. We mainly devote ourselves to the study of algebraic characterizations of its relation of elementary equivalence by providing some Keisler-Shelah type ultrapower theorems and an Ehrenfeucht-Fraı̈ssé type theorem. We also give characterizations of elementary classes in equalityfree logic...

Norm-Observable Operator Models

Hidden Markov models (HMMs) are one of the most popular and successful statistical models for time series. Observable operator models (OOMs) are generalizations of HMMs that exhibit several attractive advantages. In particular, a variety of highly efficient, constructive, and asymptotically correct learning algorithms are available for OOMs. However, the OOM theory suffers from the negative pro...

Denseness for norm attaining operator-valued functions

In this note we offer a short, constructive proof for Hilbert spaces of Lindenstrauss’ famous result on the denseness of norm attaining operators. Specifically, we show given any A ∈ L(H) there is a sequence of rank-1 operators Kn such that A+Kn is norm attaining for each n and Kn converges in norm to zero. We then apply our construction to establish denseness results for norm attaining operato...