共查询到20条相似文献,搜索用时 46 毫秒
1.
J.M. Calabuig E.A. Sánchez-Pérez 《Journal of Mathematical Analysis and Applications》2011,373(1):316-321
Let X be a Banach space and E an order continuous Banach function space over a finite measure μ. We prove that an operator T in the Köthe-Bochner space E(X) is a multiplication operator (by a function in L∞(μ)) if and only if the equality T(g〈f,x∗〉x)=g〈T(f),x∗〉x holds for every g∈L∞(μ), f∈E(X), x∈X and x∗∈X∗. 相似文献
2.
B.P. Duggal 《Journal of Mathematical Analysis and Applications》2008,340(1):366-373
A Banach space operator T∈B(X) is hereditarily polaroid, T∈HP, if every part of T is polaroid. HP operators have SVEP. It is proved that if T∈B(X) has SVEP and R∈B(X) is a Riesz operator which commutes with T, then T+R satisfies generalized a-Browder's theorem. If, in particular, R is a quasi-nilpotent operator Q, then both T+Q and T∗+Q∗ satisfy generalized a-Browder's theorem; furthermore, if Q is injective, then also T+Q satisfies Weyl's theorem. If A∈B(X) is an algebraic operator which commutes with the polynomially HP operator T, then T+N is polaroid and has SVEP, f(T+N) satisfies generalized Weyl's theorem for every function f which is analytic on a neighbourhood of σ(T+N), and f∗(T+N) satisfies generalized a-Weyl's theorem for every function f which is analytic on, and constant on no component of, a neighbourhood of σ(T+N). 相似文献
3.
A list-assignment L to the vertices of G is an assignment of a set L(v) of colors to vertex v for every v∈V(G). An (L,d)∗-coloring is a mapping ? that assigns a color ?(v)∈L(v) to each vertex v∈V(G) such that at most d neighbors of v receive color ?(v). A graph is called (k,d)∗-choosable, if G admits an (L,d)∗-coloring for every list assignment L with |L(v)|≥k for all v∈V(G). In this note, it is proved that every plane graph, which contains no 4-cycles and l-cycles for some l∈{8,9}, is (3,1)∗-choosable. 相似文献
4.
Alejandro Velez Santiago 《Journal of Mathematical Analysis and Applications》2010,372(1):120-698
Let p∈(1,N), Ω⊂RN a bounded W1,p-extension domain and let μ be an upper d-Ahlfors measure on ∂Ω with d∈(N−p,N). We show in the first part that for every p∈[2N/(N+2),N)∩(1,N), a realization of the p-Laplace operator with (nonlinear) generalized nonlocal Robin boundary conditions generates a (nonlinear) strongly continuous submarkovian semigroup on L2(Ω), and hence, the associated first order Cauchy problem is well posed on Lq(Ω) for every q∈[1,∞). In the second part we investigate existence, uniqueness and regularity of weak solutions to the associated quasi-linear elliptic equation. More precisely, global a priori estimates of weak solutions are obtained. 相似文献
5.
Francisco Odair de Paiva Eugenio Massa 《Journal of Mathematical Analysis and Applications》2008,342(1):638-650
We consider the Dirichlet problem for the equation −Δu=λu±f(x,u)+h(x) in a bounded domain, where f has a sublinear growth and h∈L2. We find suitable conditions on f and h in order to have at least two solutions for λ near to an eigenvalue of −Δ. A typical example to which our results apply is when f(x,u) behaves at infinity like a(x)|u|q−2u, with M>a(x)>δ>0, and 1<q<2. 相似文献
6.
Jian-Lin Li 《Journal of Functional Analysis》2008,255(11):3125-3148
The self-affine measure μM,D corresponding to an expanding matrix M∈Mn(R) and a finite subset D⊂Rn is supported on the attractor (or invariant set) of the iterated function system {?d(x)=M−1(x+d)}d∈D. The spectral and non-spectral problems on μM,D, including the spectrum-tiling problem implied in them, have received much attention in recent years. One of the non-spectral problem on μM,D is to estimate the number of orthogonal exponentials in L2(μM,D) and to find them. In the present paper we show that if a,b,c∈Z, |a|>1, |c|>1 and ac∈Z?(3Z),
7.
Serguei V. Astashkin 《Journal of Functional Analysis》2009,256(12):4071-4094
Let X be a rearrangement invariant function space on [0,1]. We consider the Rademacher multiplicator space Λ(R,X) of all measurable functions x such that x⋅h∈X for every a.e. converging series h=∑anrn∈X, where (rn) are the Rademacher functions. We study the situation when Λ(R,X) is a rearrangement invariant space different from L∞. Particular attention is given to the case when X is an interpolation space between the Lorentz space Λ(φ) and the Marcinkiewicz space M(φ). Consequences are derived regarding the behaviour of partial sums and tails of Rademacher series in function spaces. 相似文献
8.
Vincent Bruneau 《Journal of Functional Analysis》2003,202(2):571-590
We prove that the estimate of the number of the eigenvalues in intervals , of the reference operator L#(h) related to a self-adjoint operator L(h) is equivalent to the estimate of the integral over [λ−δ,λ+δ] of the sum of harmonic measures associated to the resonances of L(h) lying in a complex neighborhood Ω of λ>0 and the number of the positive eigenvalues of L(h) in [λ−δ,λ+δ]. We apply this result to obtain a Breit-Wigner approximation of the derivative of the spectral shift function near critical energy levels. 相似文献
9.
On derivable mappings 总被引:1,自引:0,他引:1
Jiankui Li 《Journal of Mathematical Analysis and Applications》2011,374(1):311-322
A linear mapping δ from an algebra A into an A-bimodule M is called derivable at c∈A if δ(a)b+aδ(b)=δ(c) for all a,b∈A with ab=c. For a norm-closed unital subalgebra A of operators on a Banach space X, we show that if C∈A has a right inverse in B(X) and the linear span of the range of rank-one operators in A is dense in X then the only derivable mappings at C from A into B(X) are derivations; in particular the result holds for all completely distributive subspace lattice algebras, J-subspace lattice algebras, and norm-closed unital standard algebras of B(X). As an application, every Jordan derivation from such an algebra into B(X) is a derivation. For a large class of reflexive algebras A on a Banach space X, we show that inner derivations from A into B(X) can be characterized by boundedness and derivability at any fixed C∈A, provided C has a right inverse in B(X). We also show that if A is a canonical subalgebra of an AF C∗-algebra B and M is a unital Banach A-bimodule, then every bounded local derivation from A into M is a derivation; moreover, every bounded linear mapping from A into B that is derivable at the unit I is a derivation. 相似文献
10.
Let be an affine R-monoid scheme. We prove that the category of dual functors (over the category of commutative R-algebras) of G-modules is equivalent to the category of dual functors of A∗-modules. We prove that G is invariant exact if and only if A∗=R×B∗ as R-algebras and the first projection A∗→R is the unit of A. If M is a dual functor of G-modules and wG?(1,0)∈R×B∗=A∗, we prove that MG=wG⋅M and M=wG⋅M⊕(1−wG)⋅M; hence, the Reynolds operator can be defined on M. 相似文献
11.
We introduce a notion of entropy solution for a scalar conservation law on a bounded domain with nonhomogeneous boundary condition: ut+divΦ(u)=f on Q=(0,T)×Ω, u(0,⋅)=u0 on Ω and “u=a on some part of the boundary (0,T)×∂Ω.” Existence and uniqueness of the entropy solution is established for any Φ∈C(R;RN), u0∈L∞(Ω), f∈L∞(Q), a∈L∞((0,T)×∂Ω). In the L1-setting, a corresponding result is proved for the more general notion of renormalised entropy solution. 相似文献
12.
B.P. Duggal 《Linear algebra and its applications》2008,428(4):1109-1116
A Hilbert space operator A∈B(H) is p-hyponormal, A∈(p-H), if |A∗|2p?|A|2p; an invertible operator A∈B(H) is log-hyponormal, A∈(?-H), if log(TT∗)?log(T∗T). Let dAB=δAB or ?AB, where δAB∈B(B(H)) is the generalised derivation δAB(X)=AX-XB and ?AB∈B(B(H)) is the elementary operator ?AB(X)=AXB-X. It is proved that if A,B∗∈(?-H)∪(p-H), then, for all complex λ, , the ascent of (dAB-λ)?1, and dAB satisfies the range-kernel orthogonality inequality ‖X‖?‖X-(dAB-λ)Y‖ for all X∈(dAB-λ)-1(0) and Y∈B(H). Furthermore, isolated points of σ(dAB) are simple poles of the resolvent of dAB. A version of the elementary operator E(X)=A1XA2-B1XB2 and perturbations of dAB by quasi-nilpotent operators are considered, and Weyl’s theorem is proved for dAB. 相似文献
13.
Najla A. Altwaijry 《Journal of Functional Analysis》2008,254(11):2866-2892
The Banach-Lie algebra L(A) of multiplication operators on the JB∗-triple A is introduced and it is shown that the hermitian part Lh(A) of L(A) is a unital GM-space the base of the dual cone in the dual GL-space ∗(Lh(A)) of which is affine isomorphic and weak∗-homeomorphic to the state space of L(A). In the case in which A is a JBW∗-triple, it is shown that tripotents u and v in A are orthogonal if and only if the corresponding multiplication operators in the unital GM-space Lh(A) satisfy
0?D(u,u)+D(v,v)?idA, 相似文献
14.
For a set A of positive integers and any positive integer n, let R1(A,n), R2(A,n) and R3(A,n) denote the number of solutions of a+a′=n with the additional restriction a,a′∈A; a,a′∈A,a<a′ and a,a′∈A,a≤a′ respectively. In this paper, we specially focus on the monotonicity of R3(A,n). Moreover, we show that there does not exist any set A⊂N such that R2(A,n) or R3(A,n) is eventually strictly increasing. 相似文献
15.
Toni Heikkinen 《Journal of Mathematical Analysis and Applications》2010,368(2):508-524
We study the extension properties of Orlicz-Sobolev functions both in Euclidean spaces and in metric measure spaces equipped with a doubling measure. We show that a set E⊂R satisfying a measure density condition admits a bounded linear extension operator from the trace space W1,Ψ(Rn)E| to W1,Ψ(Rn). Then we show that a domain, in which the Sobolev embedding theorem or a Poincaré-type inequality holds, satisfies the measure density condition. It follows that the existence of a bounded, possibly non-linear extension operator or even the surjectivity of the trace operator implies the measure density condition and hence the existence of a bounded linear extension operator. 相似文献
16.
Jiankui Li 《Linear algebra and its applications》2010,432(1):5-322
For a commutative subspace lattice L in a von Neumann algebra N and a bounded linear map f:N∩algL→B(H), we show that if Af(B)C=0 for all A,B,C∈N∩algL satisfying AB=BC=0, then f is a generalized derivation. For a unital C∗-algebra A, a unital Banach A-bimodule M, and a bounded linear map f:A→M, we prove that if f(A)B=0 for all A,B∈A with AB=0, then f is a left multiplier; as a consequence, every bounded local derivation from a C∗-algebra to a Banach A-bimodule is a derivation. We also show that every local derivation on a semisimple free semigroupoid algebra is a derivation and every local multiplier on a free semigroupoid algebra is a multiplier. 相似文献
17.
Françoise Lust-Piquard 《Journal of Functional Analysis》2007,244(2):488-503
We prove the little Grothendieck theorem for any 2-convex noncommutative symmetric space. Let M be a von Neumann algebra equipped with a normal faithful semifinite trace τ, and let E be an r.i. space on (0,∞). Let E(M) be the associated symmetric space of measurable operators. Then to any bounded linear map T from E(M) into a Hilbert space H corresponds a positive norm one functional f∈E(2)∗(M) such that
18.
Let E be a real separable Banach space, E∗ the dual space of E, and Ω⊂E an open bounded subset, and let T:D(T)⊆E→2E∗ be a finite dimensional upper hemi-continuous mapping with . A generalized degree theory is constructed for such a mapping. This degree is then applied to study the existence of approximate weak solutions to the equation 0∈Tx. 相似文献
19.
Jian YuDingtao Peng Shuwen Xiang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6326-6332
Let X be a nonempty, convex and compact subset of normed linear space E (respectively, let X be a nonempty, bounded, closed and convex subset of Banach space E and A be a nonempty, convex and compact subset of X) and f:X×X→R be a given function, the uniqueness of equilibrium point for equilibrium problem which is to find x∗∈X (respectively, x∗∈A) such that f(x∗,y)≥0 for all y∈X (respectively, f(x∗,y)≥0 for all y∈A) is studied with varying f (respectively, with both varying f and varying A). The results show that most of equilibrium problems (in the sense of Baire category) have unique equilibrium point. 相似文献
20.
It is well known that the commutator Tb of the Calderón-Zygmund singular integral operator is bounded on Lp(Rn) for 1 < p < +∞ if and only if b ∈ BMO [1]. On the other hand, the commutator Tb is bounded from H1(Rn) into L1(Rn) only if the function b is a constant [2]. In this article, we will discuss the boundedness of commutator of certain pseudo-differential operators on Hardy spaces H1. Let Tσ be the operators that its symbol is S01,δ with 0 ≤ δ < 1, if b ∈ LMO∞, then, the commutator [b, Tσ] is bounded from H1(Rn) into L1(Rn) and from L1(Rn) into BMO(Rn); If [b, Tσ] is bounded from H1(Rn) into L1(Rn) or L1(Rn) into BMO(Rn), then, b ∈ LMOloc. 相似文献