In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and ...

The identity problem is intractable. To shed light on the problem, which currently is a swirl of interlocking problems that tend to get tumbled together in any discussion, we separate out the various issues so they can be rationally addressed one at a time as much as possible. We explore various aspects of the problem, pick one aspect to focus on, pose an idealized theoretical solution, and the...

We show that the diagonal matrix elements of the effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at t > t0 (t0 is the instant of creation of the pair) when the total system under consideration is CPT invariant but CP noninvariant. To achieve this we use the transition amplitudes for transitions |1 >→ |2 ...

In this paper we investigate the unbounded Kasparov product between a differentiable module and an cycle of very general kind that includes all modules hence also spectral triples. Our assumptions on are weak do in particular not require it satisfies any smooth projectivity conditions. The algebras work with furthermore required to possess approximate identity. lack adequate condition our entai...

An equation over a group G is an expression of formw1 . . . wk = 1G, where eachwi is either a variable, an inverted variable, or a group constant and 1G denotes the identity element; such an equation is satisfiable if there is a setting of the variables to values in G such that the equality is realized (Engebretsen et al. (2002) [10]). In this paper, we study the problem of simultaneously satis...

BACKGROUND Multiplication of data sources within heterogeneous healthcare information systems always results in redundant information, split among multiple databases. Our objective is to detect exact and approximate duplicates within identity records, in order to attain a better quality of information and to permit cross-linkage among stand-alone and clustered databases. Furthermore, we need to...

Abstract We prove that for a Banach algebra A having bounded $\mathcal {Z}(A)$ -approximate identity and every $\mathbf {[IN]}$ group G with weight w which is either constant on conjugacy classes or satisfies $w \geq 1$ , {Z}(L^{1}_{w}(G) \otimes ^{\gamma } A) \cong \mathcal {Z}(L^{1}_{w}(G)) . As an application, we discuss the conditions under {Z}(L^{1}_{\omega }(G,A))$ enjoys certain algebrai...