共查询到20条相似文献,搜索用时 468 毫秒
1.
A.B. Aleksandrov 《Journal of Functional Analysis》2010,258(11):3675-5251
This is a continuation of our paper [2]. We prove that for functions f in the Hölder class Λα(R) and 1<p<∞, the operator f(A)−f(B) belongs to Sp/α, whenever A and B are self-adjoint operators with A−B∈Sp. We also obtain sharp estimates for the Schatten-von Neumann norms ‖f(A)−f(B)Sp/α‖ in terms of ‖A−BSp‖ and establish similar results for other operator ideals. We also estimate Schatten-von Neumann norms of higher order differences . We prove that analogous results hold for functions on the unit circle and unitary operators and for analytic functions in the unit disk and contractions. Then we find necessary conditions on f for f(A)−f(B) to belong to Sq under the assumption that A−B∈Sp. We also obtain Schatten-von Neumann estimates for quasicommutators f(A)R−Rf(B), and introduce a spectral shift function and find a trace formula for operators of the form f(A−K)−2f(A)+f(A+K). 相似文献
2.
Let B(X) be the algebra of all bounded linear operators on the Banach space X, and let N(X) be the set of nilpotent operators in B(X). Suppose ?:B(X)→B(X) is a surjective map such that A,B∈B(X) satisfy AB∈N(X) if and only if ?(A)?(B)∈N(X). If X is infinite dimensional, then there exists a map f:B(X)→C?{0} such that one of the following holds:
- (a)
- There is a bijective bounded linear or conjugate-linear operator S:X→X such that ? has the form A?S[f(A)A]S-1.
- (b)
- The space X is reflexive, and there exists a bijective bounded linear or conjugate-linear operator S : X′ → X such that ? has the form A ? S[f(A)A′]S−1.
3.
Let Mn(R) be the linear space of all n×n matrices over the real field R. For any A∈Mn(R), let ρ(A) and ‖A‖∞ denote the spectral radius and the infinity norm of A, respectively. By introducing a class of transformations φa on Mn(R), we show that, for any A∈Mn(R), ρ(A)<‖A‖∞ if . If A∈Mn(R) is nonnegative, we prove that ρ(A)<‖A‖∞ if and only if , and ρ(A)=‖A‖∞ if and only if the transformation φ‖A‖∞ preserves the spectral radius and the infinity norm of A. As an application, we investigate a class of linear discrete dynamic systems in the form of X(k+1)=AX(k). The asymptotical stability of the zero solution of the system is established by a simple algebraic method. 相似文献
4.
We study the bifurcation diagrams of classical positive solutions u with ‖u‖∞∈(0,∞) of the p-Laplacian Dirichlet problem
5.
Gabriel Padilla 《Topology and its Applications》2007,154(15):2764-2770
A classical result says that a free action of the circle S1 on a topological space X is geometrically classified by the orbit space B and by a cohomological class e∈H2(B,Z), the Euler class. When the action is not free we have a difficult open question:
- (Π)
- “Is the space X determined by the orbit space B and the Euler class?”
- •
- the intersection cohomology of X,
- •
- the real homotopy type of X.
6.
We show that every abelian topological group contains many interesting sets which are both compact and sequentially compact. Then we can deduce some useful facts, e.g.,
- (1)
- if G is a Hausdorff abelian topological group and μ:N2→G is countably additive, then the range μ(N2)={μ(A):A⊆N} is compact metrizable;
- (2)
- if X is a Hausdorff locally convex space and {xj}⊂X, then F={∑j∈Δxj:Δ⊂N, Δ is finite} is relatively compact in (X,weak) if and only if F is relatively compact in X, and if and only if F is relatively compact in (X,F(M)) where F(M) is the Dierolf topology which is the strongest 〈X,X′〉-polar topology having the same subseries convergent series as the weak topology.
7.
For 0<p<+∞ let hp be the harmonic Hardy space and let bp be the harmonic Bergman space of harmonic functions on the open unit disk U. Given 1?p<+∞, denote by ‖⋅bp‖ and ‖⋅hp‖ the norms in the spaces bp and hp, respectively. In this paper, we establish the harmonic hp-analogue of the known isoperimetric type inequality ‖fb2p‖?‖fhp‖, where f is an arbitrary holomorphic function in the classical Hardy space Hp. We prove that for arbitrary p>1, every function f∈hp satisfies the inequality
‖fb2p‖?ap‖fhp‖, 相似文献
8.
Ana Portilla Yamilet Quintana Eva Tourís 《Journal of Mathematical Analysis and Applications》2007,334(2):1167-1198
We characterize the set of functions which can be approximated by continuous functions with the norm ‖f‖L∞(w) for every weight w. This fact allows to determine the closure of the space of polynomials in L∞(w) for every weight w with compact support. We characterize as well the set of functions which can be approximated by smooth functions with the norm
‖f‖W1,∞(w0,w1):=‖f‖L∞(w0)+‖f′‖L∞(w1), 相似文献
9.
10.
11.
Surjit Singh Khurana 《Journal of Mathematical Analysis and Applications》2009,350(1):290-293
Let X be a completely regular Hausdorff space, E Hausdorff a quasi-complete locally convex space and Cb(X,E) all E-valued bounded continuous functions on X with strict topologies βt, , . We prove that a linear continuous mapping T:Cb(X,E)→E arises from a scalar measure μ∈(Cb′(X),βz)(z=t,∞,τ) if and only if g(T(f))=0 whenever g○f=0 for any f∈Cb(X,E), g∈E′. 相似文献
12.
Karim Belaid 《Topology and its Applications》2011,158(15):1969-1975
In this paper, a characterization is given for compact door spaces. We, also, deal with spaces X such that a compactification K(X) of X is submaximal or door.Let X be a topological space and K(X) be a compactification of X.We prove, here, that K(X) is submaximal if and only if for each dense subset D of X, the following properties hold:
- (i)
- D is co-finite in K(X);
- (ii)
- for each x∈K(X)?D, {x} is closed.
13.
Let ?>0. A continuous linear operator T:C(X)?C(Y) is said to ?-preserve disjointness if ‖(Tf)(Tg)‖∞≤?, whenever f,g∈C(X) satisfy ‖f‖∞=‖g‖∞=1 and fg≡0. In this paper we continue our study of the minimal interval where the possible maximal distance from a norm one operator which ?-preserves disjointness to the set of weighted composition maps may lie. We provide sharp bounds for both the finite and the infinite case, which turn out to be completely different. 相似文献
14.
Let F be a field and let m and n be integers with m,n?3. Let Mn denote the algebra of n×n matrices over F. In this note, we characterize mappings ψ:Mn→Mm that satisfy one of the following conditions:
- 1.
- |F|=2 or |F|>n+1, and ψ(adj(A+αB))=adj(ψ(A)+αψ(B)) for all A,B∈Mn and α∈F with ψ(In)≠0.
- 2.
- ψ is surjective and ψ(adj(A-B))=adj(ψ(A)-ψ(B)) for every A,B∈Mn.
15.
16.
Horst Herrlich 《Topology and its Applications》2011,158(17):2279-2286
Within the framework of Zermelo-Fraenkel set theory ZF, we investigate the set-theoretical strength of the following statements:
- (1)
- For every family(Ai)i∈Iof sets there exists a family(Ti)i∈Isuch that for everyi∈I(Ai,Ti)is a compactT2space.
- (2)
- For every family(Ai)i∈Iof sets there exists a family(Ti)i∈Isuch that for everyi∈I(Ai,Ti)is a compact, scattered, T2space.
- (3)
- For every set X, every compactR1topology (itsT0-reflection isT2) on X can be enlarged to a compactT2topology.
- (a)
- (1) implies every infinite set can be split into two infinite sets.
- (b)
- (2) iff AC.
- (c)
- (3) and “there exists a free ultrafilter” iff AC.
17.
Thierry Fack 《Journal of Functional Analysis》2004,207(2):358-398
Let M be a II∞-factor and denote by τ its normal faithful semi-finite trace. For any rearrangement invariant Köthe function space X on [0,+∞[, let X(M,τ) be the associated non-commutative Banach function space. This paper is concerned with ideals in M of the form IX(M,τ)=M∩X(M,τ) that are contained in Lp(M,τ) for some p>0. It is proved that an element T in IX(M,τ) is a finite sum of commutators of the form [A,B] with A∈IX(M,τ) and B∈M if and only if the function belongs to X, where νT is the Brown spectral measure of T and t→λt(T) is the non-increasing rearrangement of the function λ→|λ| with respect to νT. This extends to general Banach function spaces a result obtained by Kalton for quasi-Banach ideals of compact operators and implies that the Dixmier's trace of a quasi-nilpotent element in L1,∞(M,τ) is always zero. 相似文献
18.
Adam J. Prze?dziecki 《Advances in Mathematics》2010,225(4):1893-1913
We construct a functor F:Graphs→Groups which is faithful and “almost” full, in the sense that every nontrivial group homomorphism FX→FY is a composition of an inner automorphism of FY and a homomorphism of the form Ff, for a unique map of graphs f:X→Y. When F is composed with the Eilenberg-Mac Lane space construction K(FX,1) we obtain an embedding of the category of graphs into the unpointed homotopy category which is full up to null-homotopic maps.We provide several applications of this construction to localizations (i.e. idempotent functors); we show that the questions:
- (1)
- Is every orthogonality class reflective?
- (2)
- Is every orthogonality class a small-orthogonality class?
19.
Let E be a real normed linear space, K be a nonempty subset of E and be a uniformly continuous generalized Φ-hemi-contractive mapping, i.e., , and there exist x∗∈F(T) and a strictly increasing function , Φ(0)=0 such that for all x∈K, there exists j(x−x∗)∈J(x−x∗) such that
〈Tx−x∗,j(x−x∗)〉?‖x−x∗‖2−Φ(‖x−x∗‖). 相似文献
20.
Let X be a reflexive Banach space which does not have the Kadec–Klee property. Then there exists a compact mapping f from the unit ball BX of X to the dual space X? such that infx∈BX‖f(x)‖>0 and 〈f(x),x〉<‖f(x)‖ for every x∈BX. 相似文献