the theory of c-frames and c-bessel mappings are the generalizationsof the theory of frames and bessel sequences. in this paper, weobtain several equivalent conditions for dual of c-bessel mappings.we show that for a c-bessel mapping $f$, a retrievalformula with respect to a c-bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-besselmapping which  wea...

The classical identification of the predual of B(H) (the algebra of all bounded operators on a Hilbert space H) with the projective operator space tensor product H⊗̂H is extended to the context of Hilbert modules over commutative von Neumann algebras. Each bounded module homomorphism b between Hilbert modules over a general C∗-algebra is shown to be completely bounded with ‖b‖cb = ‖b‖. The so ca...

We investigate how a C*-algebra could consist of functions on a noncommutative set: a discretization of a C*-algebra A is a ∗-homomorphism A → M that factors through the canonical inclusion C(X) ⊆ `∞(X) when restricted to a commutative C*-subalgebra. Any C*-algebra admits an injective but nonfunctorial discretization, as well as a possibly noninjective functorial discretization, where M is a C*...

Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic non-perturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field algebra in which the stability group of the light-front is implemented by unitary transformations. The Hilbert space representation of states is generated by th...

It is known that a continuous family of compact operators can be diagonalized pointwise. One can consider this fact as a possibility of di-agonalization of the compact operators in Hilbert modules over a com-mutative W *-algebra. The aim of the present paper is to generalize this fact for a finite W *-algebra A not necessarily commutative. We prove that for a compact operator K acting in the ri...

The algebras Qn describe the relationship between the roots and coefficients of a non-commutative polynomial. I.Gelfand, S.Gelfand, and V. Retakh have defined quotients of these algebras corresponding to graphs. In this work we find the Hilbert series of the class of algebras corresponding to the n-vertex path, Pn. We also show this algebra is Koszul. We do this by first looking at class of qua...

Let A be a separable unital C*-algebra and let π : A → L(H) be a faithful representation of A on a separable Hilbert space H such that π(A) ∩ K(H) = {0}. We show that OE , the Cuntz-Pimsner algebra associated to the Hilbert A-bimodule E = H⊗C A, is simple and purely infinite. If A is nuclear and belongs to the bootstrap class to which the UCT applies, then the same applies to OE . Hence by the ...

In this Letter I stress the role of causal reversibility (time symmetry), together with causality and locality, in the justification of the quantum formalism. First, in the algebraic quantum formalism, I show that the assumption of reversibility implies that the observables of a quantum theory form an abstract real C^{⋆} algebra, and can be represented as an algebra of operators on a real Hilbe...

The three-dimensional quantum Euclidean space is an example of a non-commutative space that is obtained from Euclidean space by q-deformation. Simultaneously, angular momentum is deformed to soq(3), it acts on the q-Euclidean space that becomes a soq(3)-module algebra this way. In this paper it is shown, that this algebra can be realized by differential operators acting on C∞ functions on R. On...