Search results for "Bounded"

On the Existence of 1-Bounded Bi-ideals with the WELLDOC Property

2015

A combinatorial condition called well distributedoccurrences, or WELLDOC for short, has been introducedrecently. The proofs that WELLDOC property holds for thefamily of Sturmian words, and more generally, for Arnoux-Rauzy words are given in two papers by Balkova et al. The WELLDOC property for bounded bi-ideals is analysed inthis paper. The existence of a 1-bounded bi-ideal over thefinite alphabet that satisfies the WELLDOC property has beenproved by the authors.

Weakly compact composition operators between algebras of bounded analytic functions

1999

Mappings of finite distortion: The zero set of the Jacobian

2003

This paper is part of our program to establish the fundamentals of the theory of mappings of finite distortion [6], [1], [8], [13], [14], [7] which form a natural generalization of the class of mappings of bounded distortion, also called quasiregular mappings. Let us begin with the definition. We assume that Ω ⊂ Rn is a connected open set. We say that a mapping f : Ω → Rn has finite distortion if:

Codimension growth of two-dimensional non-associative algebras

2007

Let F be a field of characteristic zero and let A be a two-dimensional non-associative algebra over F. We prove that the sequence c n (A), n =1,2,..., of codimensions of A is either bounded by n + 1 or grows exponentially as 2 n . We also construct a family of two-dimensional algebras indexed by rational numbers with distinct T-ideals of polynomial identities and whose codimension sequence is n + 1, n > 2.

Factorization of homomorphisms through H∞(D)

2003

AbstractWeakly compact homomorphisms between (URM) algebras with connected maximal ideal space are shown to factor through H∞(D) by means of composition operators and to be strongly nuclear. The spectrum of such homomorphisms is also described. Strongly nuclear composition operators between algebras of bounded analytic functions are characterized. The path connected components of the space of endomorphisms on H∞(D) in the uniform operator topology are determined.

Some Questions of Heinrich on Ultrapowers of Locally Convex Spaces

1993

In this note we treat some open problems of Heinrich on ultrapowers of locally convex spaces. In section 1 we investigate the localization of bounded sets in the full ultrapower of a locally convex space, in particular the coincidence of the full and the bounded ultrapower, mainly concentrating in the case of (DF)-spaces. In section 2 we provide a partial answer to a question of Heinrich on commutativity of strict inductive limits and ultrapowers. In section 3 we analyze the relation between some natural candidates for the notion of superreflexivity in the setting of Frechet spaces. We give an example of a Frechet-Schwartz space which is not the projective limit of a sequence of superreflex…

Derived categories of irreducible projective curves of arithmetic genus one

2006

We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact auto-equivalences and the set of all $t$ -structures of this category is given. We describe the moduli space of stability conditions, obtain a complete classification of all spherical objects in this category and show that the group of exact auto-equivalences acts transitively on them. Harder–Narasimhan filtrations in the sense of Bridgeland are used as our main technical tool.

Functional calculi for convolution operators on a discrete, periodic, solvable group

2009

Suppose T is a bounded self-adjoint operator on the Hilbert space L2(X,μ) and let T=∫SpL2TλdE(λ) be its spectral resolution. Let F be a Borel bounded function on [−a,a], SpL2T⊂[−a,a]. We say that F is a spectral Lp-multiplier for T, if F(T)=∫SpL2TF(λ)dE(λ) is a bounded operator on Lp(X,μ). The paper deals with l1-multipliers, where X=G is a discrete (countable) solvable group with ∀x∈G, x4=1, μ is the counting measure and TΦ:l2(G)∋ξ↦ξ∗Φ∈l2(G), where Φ=Φ∗ is a l1(G) function, suppΦ generates G. The main result of the paper states that there exists a Ψ on G such that all l1-multipliers for TΨ are real analytic at every interior point of Spl2(G)TΨ. We also exhibit self-adjoint Φ′s in l1(G) suc…

BLD -mappings in $W^{2,2}$ are locally invertible

2000

We prove that mappings of bounded length distortion are local homeomorphisms if they have L 2 -integrable weak second derivatives.

Logical definability of NP-optimisation problems with monadic auxiliary predicates

1993

Given a first-order formula ϕ with predicate symbols e1...el, so,...,sr, an NP-optimisation problem on -structures can be defined as follows: for every -structure G, a sequence of relations on G is a feasible solution iff satisfies ϕ, and the value of such a solution is defined to be ¦S0¦. In a strong sense, every polynomially bounded NP-optimisation problem has such a representation, however, it is shown here that this is no longer true if the predicates s1, ...,sr are restricted to be monadic. The result is proved by an Ehrenfeucht-Fraisse game and remains true in several more general situations.