We formulate the dynamics of an infinitely extended open dissipative quantum system , Σ, in Schroedinger picture. The generic model on which this is based comprises a C★-algebra, A observables, folium, ℱ states algebra and one-parameter semigroup, τ linear transformations that represents its given by natural infinite-volume limit corresponding semigroup for finite system. On basis, we establish...

in the present paper, we consider biflatness of certain classes of semigroupalgebras. indeed, we give a necessary condition for a band semigroup algebra to bebiflat and show that this condition is not sufficient. also, for a certain class of inversesemigroups s, we show that the biflatness of ell^{1}(s)^{primeprime} is equivalent to the biprojectivity of ell^{1}(s).

Abstract We give rigidity results for the discrete Bonnet–Myers diameter bound and Lichnerowicz eigenvalue estimate. Both inequalities are sharp if only underlying graph is a hypercube. The proofs use well-known semigroup methods as well new direct which translate curvature to combinatorial properties. Our can be seen first known analogues of Cheng’s Obata’s theorems.

For any affine semigroup S, the set S∪{∞} has a natural structure; additionally, if S is endowed with discrete topology, then can be studied as one-point compactification of S. In this article, we study derivations on algebra C[S∪{∞}] in relation to C[S] considering metrizable topology induced by S∪{∞}.

The main purpose of this paper is to establish a relation between universality of certain P-compactifications of a semitopological semigroup and their corresponding enveloping semigroups. In particular, we show that if we take P to be the property that the enveloping semigroup of a compactification of a semitopological semigroup s is left simple, a group, or the trivial singleton semigroup, t...

Given a Hamiltonian H on a Hilbert space H it is shown that, under the assumption that σ(H) = σac(H) = R , there exist unique positive operators TF and TB registering the Schrödinger time evolution generated by H in the forward (future) direction and backward (past) direction respectively. These operators may be considered as time observables for the quantum evolution. Moreover, it is shown tha...

We prove the quantum conditional Entropy Power Inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional entropies of the input state and the noise when they are conditionally independent given the memory. We also show that this conditional Entropy Power Inequality i...

We investigate the notion of Connes-amenability, introduced by Runde in [14], for bidual algebras and weighted semigroup algebras. We provide some simplifications to the notion of a σWC-virtual diagonal, as introduced in [10], especially in the case of the bidual of an Arens regular Banach algebra. We apply these results to discrete, weighted, weakly cancellative semigroup algebras, showing tha...