We obtain a complete description of closed ideals of the algebra D ∩ lip α , 0 < α ≤ 1 2 , where D is the Dirichlet space and lip α is the algebra of analytic functions satisfying the Lipschitz condition of order α.

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...

In this paper, we determine the character space of vector-valued Lipschitz algebra Lipd(X, E), where (X, d) is any metric and E a certain unital semisimple commutative *-Banach algebra.

Let U be an open relatively compact subanalytic subset of a real analytic manifold. We show that there exists a finite linear covering (in the sense of Guillermou and Schapira) of U by subanalytic open subsets of U homeomorphic to a unit ball. We also show that the algebra of open relatively compact subanalytic subsets of a real analytic manifold is generated by subsets subanalytically and bi-l...

Abstract Each vector space that is endowed with a quadratic form determines its Clifford algebra. This algebra, in turn, contains distinguished group, known as the Lipschitz group. We show only quotient of this group remains meaningful context projective metric geometry. can be viewed point set on algebra and, under certain restrictions, leads to an algebraic description so-called kinematic map...

We introduce the Fourier-Stieltjes algebra in Rn which we denote by FS(Rn). It is a subalgebra of the algebra of bounded uniformly continuous functions in Rn, BUC(Rn), strictly containing the almost periodic functions, whose elements are invariant by translations and possess a mean-value. Thus, it is a so called algebra with mean value, a concept introduced by Zhikov and Krivenko (1986). Namely...

We present an operator space version of Rieffel’s theorem on the agreement of the metric topology, on a subset of the Banach space dual of a normed space, from a seminorm with the weak*-topology. As an application we obtain a necessary and sufficient condition for the matrix metric from an unbounded Fredholm module to give the BW-topology on the matrix state space of the C-algebra. Motivated by...