# Centrality measure for positive elements of W*-algebras

@inproceedings{Novikov2020CentralityMF, title={Centrality measure for positive elements of W*-algebras}, author={A. V. Novikov and Sami Abdullah Abed and Irina Nikolaeva}, year={2020} }

In this article we propose a measure that gives an answer “How far is an element from central?” We introduce the definition for the measure of centrality of the von Neumann algebra (W ∗-algebra) elements and give the formula for the countably decomposable algebras. Particularly, that means that we gave measure of centrality for block diagonal matrices. We think that this article could be useful in the research of perturbations applied to inequalities characterizing traces and central elements.

## References

SHOWING 1-10 OF 36 REFERENCES

Connections between centrality and local monotonicity of certain functions on C⁎-algebras

- Mathematics, Physics
- 2016

Abstract We introduce a quite large class of functions (including the exponential function and the power functions with exponent greater than one), and show that for any element f of this function…

Commutativity of projections and characterization of traces on Von Neumann algebras

- Mathematics
- 2010

We find new necessary and sufficient conditions for the commutativity of projections in terms of operator inequalities. We apply these inequalities to characterize a trace on von Neumann algebras in…

Characterization of central elements of operator algebras by inequalities

- Mathematics
- 2015

We propose a list of inequalities which characterize central elements in von Neumann algebras and C*-algebras.

Limits of the Banach spaces associated with positive operator $a$ affiliated with von Neumann algebra, which are neither purely projective nor purely inductive

- Mathematics
- 2019

We consider linear normed spaces of opearators dominated by positive operator affiliated with the von Neumann algebra powered by real positive parameter. We consider and define different natural…

Commutativity of operators and characterization of traces on C*-algebras

- Mathematics
- 2013

79 This paper continues the author’s study begun in [1, 2]; we retain the notation and terminology used there. In Section 2, we give new criteria for the com� mutativity of a nonnegative operator and…

Inequalities for Determinants and Characterization of the Trace

- Mathematics
- 2020

Let tr be the canonical trace on the full matrix algebra $${{\cal M}_n}$$ ℳ n with unit I . We prove that if some analog of classical inequalities for the determinant and trace (or the permanent and…

L1-space for a positive operator affiliated with von Neumann algebra

- 2018

In this paper we suggest an approach for constructing an L1-type space for a positive selfadjoint operator affiliated with von Neumann algebra. For such operator we introduce a seminorm, and prove…

Subadditivity Inequalities in von Neumann Algebras and Characterization of Tracial Functionals

- Mathematics, Chemistry
- 2002

AbstractWe examine under which assumptions on a positive normal functional φ on a von Neumann algebra,
$${\cal M}$$ and a Borel measurable function f: R+ → R with f(0) = 0 the subadditivity…

C*-algebra Positive Element Invertibility Criteria in Terms of L1-norms Equivalence and L∞-norms Equivalence

- MathematicsLobachevskii Journal of Mathematics
- 2019

We prove that the L1-norms associated with a positive elements aα is equivalent to the L1-norm associated with a positive element aβ if and only if it is equivalent to the natural norm of a…

Fundamentals of the Theory of Operator Algebras

- Mathematics
- 1983

Comparison theory of projections--exercises and solutions Normal states and unitary equivalence of von Neumann algebras--exercises and solutions The trace--exercises and solutions Algebra and…