共查询到20条相似文献,搜索用时 15 毫秒
1.
Bebe Prunaru 《Journal of Functional Analysis》2008,254(6):1626-1641
Let H be a complex Hilbert space and let {Tn}n?1 be a sequence of commuting bounded operators on H such that . Let denote the space of all operators X in B(H) for which and suppose that . We will show that there exists a triple {K,Γ,{Un}n?1} where K is a Hilbert space, Γ:K→H is a bounded operator and {Un}n?1⊂B(K) is a sequence of commuting normal operators with such that TnΓ=ΓUn for n?1, and for which the mapping Y?ΓYΓ∗ is a complete isometry from the commutant of {Un}n?1 onto the space . Moreover we show that the inverse of this mapping can be extended to a ∗-homomorphism
2.
Salah Mecheri Messaoud Bounkhel 《Journal of Mathematical Analysis and Applications》2003,287(1):51-60
In this paper we characterize the global minimum of an arbitrary function defined on a Banach space, in terms of a new concept of derivatives adapted for our case from a recent work due to D.J. Keckic (J. Operator Theory, submitted for publication). Using these results we establish several new characterizations of the global minimum of the map defined by Fψ(X)=‖ψ(X)‖1, where is a map defined by ψ(X)=S+φ(X) and φ:B(H)→B(H) is a linear map, S∈C1, and . Further, we apply these results to characterize the operators which are orthogonal to the range of elementary operators. 相似文献
3.
In this paper we discuss the asymptotic distribution of the approximation numbers of the finite sections for a Toeplitz operator T(a)∈L(?p), 1<p<∞, where a is a piecewise continuous function on the unit circle. We prove that the behavior of the approximation numbers of the finite sections Tn(a)=PnT(a)Pn depends heavily on the Fredholm properties of the operators T(a) and . In particular, if the operators T(a) and are Fredholm on ?p, then the approximation numbers of Tn(a) have the so-called k-splitting property. But, in contrast with the case of continuous symbols, the splitting number k is in general larger than . 相似文献
4.
Hyoung Joon Kim 《Journal of Mathematical Analysis and Applications》2009,350(1):262-270
In this paper, we employ the model theory due to C. Foias and C. Pearcy and the notion of Enflo's extremal vectors of quasinilpotent operators to study the hyperinvariant subspace problem for quasinilpotent operators. Our main result is that if a quasinilpotent quasiaffinity T has a sequence of “c-eigenvectors” xn of TnT∗n such that the set is compact, then T has a nontrivial hyperinvariant subspace. 相似文献
5.
Xiaosong Liu 《Journal of Mathematical Analysis and Applications》2006,324(1):604-614
Suppose f is a spirallike function of type β (or starlike function of order α) on the unit disk D in C. Let , where 1?p1?2 (or 0<p1?2), pj?1, j=2,…,n, are real numbers. In this paper, we prove that
6.
Let K1,…,Kn be (infinite) non-negative matrices that define operators on a Banach sequence space. Given a function f:[0,∞)×…×[0,∞)→[0,∞) of n variables, we define a non-negative matrix and consider the inequality
7.
Mohamed Barraa Mohamed Boumazgour 《Journal of Mathematical Analysis and Applications》2003,286(1):359-362
Let be the algebra of bounded linear operators on a Hilbert space H. For , define the elementary operator MA,B by MA,B(X)=AXB (). We give necessary and sufficient conditions for any pair of operators A and B to satisfy the equation ‖I+MA,B‖=1+‖A‖‖B‖, where I is the identity operator on H. 相似文献
8.
Antoine Derighetti 《Journal of Functional Analysis》2004,215(2):341-365
Let G be a locally compact group and let p∈(1,∞). Let be any of the Banach spaces Cδ,p(G), PFp(G), Mp(G), APp(G), WAPp(G), UCp(G), PMp(G), of convolution operators on Lp(G). It is shown that PFp(G)′ can be isometrically embedded into UCp(G)′. The structure of maximal regular ideals of (and of MAp(G)″, Bp(G)″, Wp(G)″) is studied. Among other things it is shown that every maximal regular left (right, two sided) ideal in is either dense or is the annihilator of a unique element in the spectrum of Ap(G). Minimal ideals of is also studied. It is shown that a left ideal M in is minimal if and only if , where Ψ is either a right annihilator of or is a topologically x-invariant element (for some x∈G). Some results on minimal right ideals are also given. 相似文献
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10.
Marian Nowak 《Journal of Mathematical Analysis and Applications》2009,349(2):361-366
Let L(X,Y) stand for the space of all bounded linear operators between real Banach spaces X and Y, and let Σ be a σ-algebra of sets. A bounded linear operator T from the Banach space B(Σ,X) of X-valued Σ-totally measurable functions to Y is said to be σ-smooth if ‖T(fn)Y‖→0 whenever a sequence of scalar functions (‖fn(⋅)X‖) is order convergent to 0 in B(Σ). It is shown that a bounded linear operator is σ-smooth if and only if its representing measure is variationally semi-regular, i.e., as An↓∅ (here stands for the semivariation of m on A∈Σ). As an application, we show that the space Lσs(B(Σ,X),Y) of all σ-smooth operators from B(Σ,X) to Y provided with the strong operator topology is sequentially complete. We derive a Banach-Steinhaus type theorem for σ-smooth operators from B(Σ,X) to Y. Moreover, we characterize countable additivity of measures in terms of continuity of the corresponding operators . 相似文献
11.
Juan F. Mena-Jurado Francisco Montiel-Aguilera 《Journal of Mathematical Analysis and Applications》2004,289(1):30-34
In this note, we characterize nice operators in a class of Banach spaces, which includes spaces and L1(μ), as those operators that preserve extreme points. 相似文献
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13.
Linear Fractional Maps of the Unit Ball: A Geometric Study 总被引:1,自引:0,他引:1
Cinzia BisiFilippo Bracci 《Advances in Mathematics》2002,167(2):265-287
14.
Pascale Vitse 《Journal of Functional Analysis》2005,228(2):245-269
It is well-known that -sectorial operators generally do not admit a bounded H∞ calculus over the right half-plane. In contrast to this, we prove that the H∞ calculus is bounded over any class of functions whose Fourier spectrum is contained in some interval [ε,σ] with 0<ε<σ<∞. The constant bounding this calculus grows as as and this growth is sharp over all Banach space operators of the class under consideration. It follows from these estimates that -sectorial operators admit a bounded calculus over the Besov algebra of the right half-plane. We also discuss the link between -sectorial operators and bounded Tadmor-Ritt operators. 相似文献
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17.
John A. Rhodes 《Journal of Number Theory》2003,102(2):278-297
We define n families of Hecke operators for GLn whose generating series are rational functions of the form qk(u)−1 where qk is a polynomial of degree , and whose form is that of the kth exterior product. This work can be viewed as a refinement of work of Andrianov (Math. USSR Sb. 12(3) (1970)), in which he defined Hecke operators the sum of whose generating series was a rational function with nontrivial numerator and whose denominator was essentially .By a careful analysis of the Satake map which defines an isomorphism between a local Hecke algebra and a ring of symmetric polynomials, we define n families of (polynomial) Hecke operators and characterize their generating series as rational functions. We then give an explicit means by which to locally invert the Satake isomorphism, and show how to translate these polynomial operators back to the classical double coset setting. The classical Hecke operators have generating series of exactly the same form as their polynomial counterparts, and hence are of number-theoretic interest. We give explicit examples for GL3 and GL4. 相似文献
18.
Let X1,X2,…,Xq be a system of real smooth vector fields satisfying Hörmander's rank condition in a bounded domain Ω of Rn. Let be a symmetric, uniformly positive definite matrix of real functions defined in a domain U⊂R×Ω. For operators of kind
19.
Yucai Su 《Advances in Mathematics》2003,174(1):57-68
For a nondegenerate additive subgroup Γ of the n-dimensional vector space over an algebraically closed field of characteristic zero, there is an associative algebra and a Lie algebra of Weyl type spanned by all differential operators uD1m1?Dnmn for (the group algebra), and m1,…,mn?0, where D1,…,Dn are degree operators. In this paper, it is proved that an irreducible quasifinite -module is either a highest or lowest weight module or else a module of the intermediate series; furthermore, a classification of uniformly bounded -modules is completely given. It is also proved that an irreducible quasifinite -module is a module of the intermediate series and a complete classification of quasifinite -modules is also given, if Γ is not isomorphic to . 相似文献
20.
In this paper, it is shown that the Berezin-Toeplitz operator Tg is compact or in the Schatten class Sp of the Segal-Bargmann space for 1?p<∞ whenever (vanishes at infinity) or , respectively, for some s with , where is the heat transform of g on Cn. Moreover, we show that compactness of Tg implies that is in C0(Cn) for all and use this to show that, for g∈BMO1(Cn), we have is in C0(Cn) for some s>0 only if is in C0(Cn) for alls>0. This “backwards heat flow” result seems to be unknown for g∈BMO1 and even g∈L∞. Finally, we show that our compactness and vanishing “backwards heat flow” results hold in the context of the weighted Bergman space , where the “heat flow” is replaced by the Berezin transform Bα(g) on for α>−1. 相似文献