Applications of Automata and Graphs: Labeling Operators in Hilbert Space II [PDF]
, 2008 We introduced a family of infinite graphs directly associated with a class of von Neumann automaton model A_{G}. These are finite state models used in symbolic dynamics: stimuli models and in control theory. In the context of groupoid von Neumann algebras, and an associated fractal group, we prove a classification theorem for representations of ...
Fannes M. +11 more
arxiv +5 more sources
On Pompeiu-Cebysev type inequalities for positive linear maps of selfadjoint operators in inner product spaces [PDF]
arXiv, 2018 In this work, generalizations of some inequalities for continuous $h$-synchronous ($h$-asynchronous) functions of linear bounded selfadjoint operators under positive linear maps in Hilbert spaces are proved.
Alomari, Mohammad W.
arxiv +5 more sources
Some Inequalities for Trace Class Operators Via a Kato's Result [PDF]
arXiv, 2014 By the use of the celebrated Kato's inequality we obtain in this paper some new inequalities for trace class operators on a complex Hilbert space H. Natural applications for functions defined by power series of normal operators are given as well.
Dragomir, Silvestru Sever
arxiv +3 more sources
Some Trace Inequalities for Operators in Hilbert Spaces [PDF]
arXiv, 2014 Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace inequalities for matrices are also derived.
Dragomir, Silvestru Sever
arxiv +3 more sources
Inequalities for Quantum f-Divergence of Trace Class Operators in Hilbert Spaces [PDF]
arXiv, 2015 Some inequalities for quantum f-divergence of trace class operators in Hilbert spaces are obtained. It is shown that for normalised convex functions it is nonnegative. Some upper bounds for quantum f-divergence in terms of variational and chi-distance are provided.
Dragomir, Sever S
arxiv +3 more sources
New counterexamples on Ritt operators, sectorial operators and R-boundedness [PDF]
arXiv, 2018 Let $\mathcal D$ be a Schauder decomposition on some Banach space $X$. We prove that if $\mathcal D$ is not $R$-Schauder, then there exists a Ritt operator $T\in B(X)$ which is a multiplier with respect to $\mathcal D$, such that the set $\{T^n\, :\, n\geq 0\}$ is not $R$-bounded.
Arnold, Loris, Merdy, Christian Le
arxiv +2 more sources
Some Jensen's Type Inequalities for Twice Differentiable Functions of Selfadjoint Operators in Hilbert Spaces [PDF]
, 2008 Some Jensen’s type inequalities for twice differentiable functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given.
Dragomir, Sever S
core +1 more source
Strictly singular operators and isomorphisms of Cartesian products of power series spaces [PDF]
, 1998 V. P. Zahariuta, in 1973, used the theory of Fredholm operators to develop a method to classify Cartesian products of locally convex spaces. In this work we modify his method to study the isomorphic classification of Cartesian products of the kind E0p(a)×
Djakov, Plamen Borissov +5 more
core +1 more source
Note on a Family of Monotone Quantum Relative Entropies [PDF]
, 2015 Given a convex function $\varphi$ and two hermitian matrices $A$ and $B$, Lewin and Sabin study in [M. Lewin, J. Sabin, {\it A Family of Monotone Quantum Relative Entropies}, Lett. Math. Phys.
Deuchert, Andreas +2 more
core +3 more sources
Isometries on extremely non-complex Banach spaces [PDF]
, 2010 Given a separable Banach space $E$, we construct an extremely non-complex Banach space (i.e. a space satisfying that $\|Id + T^2\|=1+\|T^2\|$ for every bounded linear operator $T$ on it) whose dual contains $E^*$ as an $L$-summand.
Koszmider, Piotr +2 more
core +1 more source