Among P-pseudo-Hermitian Hamiltonians H = P−1H† P with real spectra, the “weakly pseudo-Hermitian” ones (i.e., those employing non-self-adjoint P 6 = P†) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever P 6 = P†, the current involutive operator of charge C gets complemented by a nonequivalent alternative involutive quasip...

In this paper, we study pseudo-valuations on a BCI-algebra and obtain some related results. The relation between pseudo-valuations and ideals is investigated. We use a pseudo-metric induced by a pseudovaluation to introduce a congruence relation on a BCI-algebra. We define the quotient algebra induced by this relation and prove that it is also a BCI-algebra and study its properties.

This paper introduces a new idea in the unital involutive Banach algebras and its closed subset. aims to study cohomology theory of operator algebra. We will algebra as an applied example algebra, be denoted by . The definitions cyclic, simplicial, dihedral group src=image/13426521_01.gif> introduced. presented definition src=image/13426521_14.gif>-relative that i...

The structure group and the involutive differential system that characterize the pseudo-group of contact transformations on a jet space are determined.

In this paper,  pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.

We show that when a co-involutive Hopf C *-algebra S coacts via δ on a C *-algebra A, there exists a full crossed product A × δ S, with universal properties analogous to those of full crossed products by locally compact groups. The dual Hopf C *-algebra is then defined byˆS := C × id S.

We consider the natural Lie algebra structure on the (associative) group algebra of a finite group G, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a decomposition in simple factors of these Lie algebras, in terms of the ordinary representations of G. MSC 2000 : 20C15,17B99.

Let C be the propositional calculus given by a standard SBL-algebra; C is obtained from C by adding an involutive negation, with axioms and deduction rules as in [4]. Then C is coNP-complete.