We show that universal algebras with factorable congruences such as rings with 1 and semirings with 0 and 1 enjoy some of the properties of universal algebras whose congruence lattices are distributive, such as the strict refinement property and a variant of Jónsson’s lemma. A universal algebra A is said to have factorable congruences if whenever A ∼= B × C and θ is a congruence on A, then θ = ...

The notion of operator-valued frames (OVFs) by Kaftal et al. (Trans Am Math Soc 361(12):6349–6385, 2009) and G-frames Sun (J Anal Appl 322(1):437–452, 2006) do not include all generalizations notions for Hilbert spaces. For this purpose, we introduce the weak (weak OVFs) which covers known Theory weak-OVFs is more demanding than theory OVFs due to following: One, frame operator may factor anoth...

There are many different ways to subdivide the spectrum of a bounded linear operator; some of them are motivated by applications to physics (in particular, quantum mechanics). In a series of papers, B.E. Rhoades and M. Yildirim previously investigated the spectra and fine spectra for factorable matrices, considered as bounded operators over various sequence spaces. In the present paper, approxi...

It has recently been argued that there are no dynamic screening corrections to Salpeter’s enhancement factor in thermonuclear reactions, in the weak-screening limit. The arguments used were: 1) The Gibbs probability distribution is factorable into two parts, one of which, exp(−β∑ eiej/rij) (β = 1/kBT ), is independent of velocity space; and 2) The enhancement factor is w = 1 + βeZ1Z2〈φ〉 with 〈φ...

0

Let Φ be a super-operator, i.e., a linear mapping of the form Φ : L(F) → L(G) for finite dimensional Hilbert spaces F and G. This paper considers basic properties of the super-operator norms defined by ‖Φ‖q→p = sup{‖Φ(X)‖p/‖X‖q : X 6= 0}, induced by Schatten norms for 1 ≤ p, q ≤ ∞. These super-operator norms arise in various contexts in the study of quantum information. In this paper it is prov...

where dA is the normalized area measure in D. The case where α = 0 is known as the (unweighted) Bergman space, often simply denoted by A2. Let φ be an analytic map from the open unit disk D into itself. The operator that takes the analytic map f to f ◦ φ is a composition operator and is denoted by Cφ . A natural generalization of a composition operator is an operator that takes f to ψ · f ◦ φ, ...

we observe that the variable φ enters the expression in the form of the operator ∂2/∂φ2. This operator—1D Laplace operator with respect to the variable φ—is a Hermitian operator in the space of single-valued functions of the angle φ, because single-valuedness is equivalent to the 2π-periodicity, and Laplace operator is Hermitian in the space of periodic functions. Hence, we have ONB of the eige...