Let A(D) be the disc algebra of all continuous complex-valued functions on the unit disc D holomorphic in its interior. Functions from A(D) act on the set of all contraction operators (‖A‖ 1) on Hilbert spaces. It is proved that the following classes of functions from A(D) coincide: (1) the class of operator Lipschitz functions on the unit circle T; (2) the class of operator Lipschitz functions...

Given a measure space 〈X,μ〉, we define its measure algebra Aμ as the quotient of the algebra of all measurable subsets of X modulo the relation X μ ∼ Y if μ(X4Y ) = 0. If further X is endowed with a topology T , we can define an interior operator on Aμ analogous to the interior operator on P(X). Formulas of S4u (the modal logic S4 with a universal modality ∀ added) can then be assigned elements...

The comprehensive generalization of summation-by-parts of Del Rey Fernández et al. (J. Comput. Phys., 266, 2014) is extended to approximations of second derivatives with variable coefficients. This enables the construction of second-derivative operators with one or more of the following characteristics: i) non-repeating interior stencil, ii) nonuniform nodal distributions, and iii) exclusion of...

We construct a Banach space operator T ∈ B(X) such that the set JT (0) has a nonempty interior but JT (0) 6= X. This gives a negative answer to a problem raised by G. Costakis and A. Manoussos.

In this paper, we obtain some general results on information retrieval from the black hole interior, based recent progress quantum extremal surface formula and entanglement island. We study an AdS coupled to a bath with generic dynamics, ask whether it is possible retrieve about small perturbation in interior system. derive state reconstruction one norm. However, show that contradiction arises ...

There have been many research developments on the conceptual description of topological relations between spatial objects. In order to practically implement these conceptual topological relations in a computer environment, we need to calculate the values of the topological relations. One of the theoretical bases for doing this is a computational fuzzy topology, which is the research focus of th...

We continue Mizar formalization of General Topology according to the book [19] by Engelking. In the article the formalization of Section 1.2 is almost completed. Namely, we formalize theorems on introduction of topologies by bases, neighborhood systems, closed sets, closure operator, and interior operator. The Sorgenfrey line is defined by a basis. It is proved that the weight of it is continuu...

It is established that an interior penalty method applied to secondorder elliptic problems gives rise to a local operator which is spectrally equivalent to the corresponding nonlocal operator arising from the mixed finite element method. This relation can be utilized in order to construct preconditioners for the discrete mixed system. As an example, a family of additive Schwarz preconditioners ...

We show that two operator algebras are strongly Morita equivalent (in the sense of Blecher, Muhly and Paulsen) if and only if their categories of operator modules are equivalent via completely contractive functors. Moreover, any such functor is completely isometrically isomorphic to the Haagerup tensor product (= interior tensor product) with a strong Morita equivalence bimodule. Date: Septembe...