Search results for "Bounded function"
showing 10 items of 508 documents
Rigidity of commutators and elementary operators on Calkin algebras
1998
LetA=(A 1,...,A n ),B=(B 1,...,B n )eL(l p ) n be arbitraryn-tuples of bounded linear operators on (l p ), with 1<p<∞. The paper establishes strong rigidity properties of the corresponding elementary operators e a,b on the Calkin algebraC(l p )≡L(l p )/K(l p ); $$\varepsilon _{\alpha ,b} (s) = \sum\limits_{i = 1}^n {a_i sb_i } $$ , where quotient elements are denoted bys=S+K(l p ) forSeL(l p ). It is shown among other results that the kernel Ker(e a,b ) is a non-separable subspace ofC(l p ) whenever e a,b fails to be one-one, while the quotient $$C(\ell ^p )/\overline {\operatorname{Im} \left( {\varepsilon _{\alpha ,b} } \right)} $$ is non-separable whenever e a,b fails to be onto. These re…
Bounded elements in certain topological partial *-algebras
2011
We continue our study of topological partial *algebras, focusing our attention to the interplay between the various partial multiplications. The special case of partial *-algebras of operators is examined first, in particular the link between the strong and the weak multiplications, on one hand, and invariant positive sesquilinear (ips) forms, on the other. Then the analysis is extended to abstract topological partial *algebras, emphasizing the crucial role played by appropriate bounded elements, called $\M$-bounded. Finally, some remarks are made concerning representations in terms of the so-called partial GC*-algebras of operators.
Boundary modulus of continuity and quasiconformal mappings
2012
Let D be a bounded domain in R n , n ‚ 2, and let f be a continuous mapping of D into R n which is quasiconformal in D. Suppose that jf(x) i f(y)j • !(jx i yj) for all x and y in @D, where ! is a non-negative non-decreasing function satisfying !(2t) • 2!(t) for t ‚ 0. We prove, with an additional growth condition on !, that jf(x) i f(y)jC maxf!(jx i yj);jx i yj fi g
ON THE COLENGTH OF A VARIETY OF LIE ALGEBRAS
1999
We study the variety of Lie algebras defined by the identity [Formula: see text] over a field of characteristic zero. We prove that, as in the associative case, in the nth cocharacter χn of this variety, every irreducible Sn-character appears with polynomially bounded multiplicity (not greater than n2). Anyway, surprisingly enough, we also show that the colength of this variety, i.e. the total number of irreducibles appearing in χn is asymptotically equal to [Formula: see text].
Surface families and boundary behavior of quasiregular mappings
2005
We study the boundary behavior of bounded quasiregular mappings f : Bn(0, 1) → Rn, n ≥ 3. We show that there exists a large family of cusps, with vertices on the boundary sphere S n−1 (0, 1), so that the images of these cusps under f have finite (n − 1)-measure. peerReviewed
A DUALITY APPROACH TO THE FRACTIONAL LAPLACIAN WITH MEASURE DATA
2011
We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like $$(-\Delta)^s v = \mu \quad \text{in } \mathbb{R}^N,$$ ¶ with vanishing conditions at infinity. Here $\mu$ is a bounded Radon measure whose support is compactly contained in $\mathbb{R}^N$, $N\geq2$, and $-(\Delta)^s$ is the fractional Laplace operator of order $s\in (1/2,1)$.
Volumes transverses aux feuilletages d'efinissables dans des structures o-minimales
2003
Let Fλ be a family of codimension p foliations defined on a family Mλ of manifolds and let Xλ be a family of compact subsets of Mλ. Suppose that Fλ, Mλ and Xλ are definable in an o-minimal structure and that all leaves of Fλ are closed. Given a definable family Ωλ of differential p-forms satisfaying iZ Ωλ = 0 forany vector field Z tangent to Fλ, we prove that there exists a constant A > 0 such that the integral of on any transversal of Fλ intersecting each leaf in at most one point is bounded by A. We apply this result to prove that p-volumes of transverse sections of Fλ are uniformly bounded.
Notions of Dirichlet problem for functions of least gradient in metric measure spaces
2019
We study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a (1, 1)-Poincaré inequality. Since one of the two notions is not amenable to the direct method of the calculus of variations, we construct, based on an approach of Juutinen and Mazón-Rossi–De León, solutions by considering the Dirichlet problem for p-harmonic functions, p>1, and letting p→1. Tools developed and used in this paper include the inner perimeter measure of a domain. Peer reviewed
Weyl's Theorems and Extensions of Bounded Linear Operators
2012
A bounded operator $T\in L(X)$, $X$ a Banach space, is said to satisfy Weyl's theorem if the set of all spectral points that do not belong to the Weyl spectrum coincides with the set of all isolated points of the spectrum which are eigenvalues and having finite multiplicity. In this article we give sufficient conditions for which Weyl's theorem for an extension $\overline T$ of $T$ (respectively, for $T$) entails that Weyl's theorem holds for $T$ (respectively, for $\overline T$).
Fixpunktmengen von halbeinfachen Automorphismen in halbeinfachen Lie-Algebren
1976
Let g be a semisimple Lie algebra over an algebraically closed field of characteristic 0. The set of fixed points of a semisimple inner automorphism of g is a regular reductive subalgebra of maximal rank [1], so it is defined by a subsystem of the root system Φ of g relative to a suitable Cartan subalgebra. The main theorem of the article characterizes the corresponding subsystems of Φ. The second part of the article shows how to compute the fixed point algebras of semisimple outer automorphisms of g. A complete list of all fixed point algebras is then easily obtainable. The results are applied to bounded symmetric domains. References