共查询到20条相似文献,搜索用时 24 毫秒
1.
Won Keun Min 《Acta Mathematica Hungarica》2012,136(1-2):129-137
Let expX be the power set of a non-empty set?X. A function γ:?expX→expX is said to be monotonic iff A?B?X implies γA?γB. Császár?[2] investigated relations between the monotonic functions. The purpose of the paper is to investigate some results concerning particular monotonic functions. 相似文献
2.
Carlos Lizama Verónica Poblete 《Journal of Mathematical Analysis and Applications》2007,327(2):1335-1359
In this paper we study multiplicative perturbations for the generator of a strongly continuous integral resolvent family of bounded linear operators defined on a Banach space X. Assuming that a(t) is a creep function which satisfies a(0+)>0, we prove that if (A,a) generates an integral resolvent, then (A(I+B),a) also generates an integral resolvent for all B∈B(X,Z), where Z belongs to a class of admissible Banach spaces. In special instances of a(t) the space Z is proved to be characterized by an extended class of Favard spaces. 相似文献
3.
J.J Buoni 《Journal of Mathematical Analysis and Applications》1976,56(1):55-60
Let T be a closed operator on a Hilbert Space H, such that α?p(T), the resolvent of T. Set A = (T ? αI)?1. For μ ≠ 0, define λ such that (λ ? α)μ = 1. It is shown that λ ? essential spectra of T iff μ ? essential spectra of A for various definitions of the essential spectra. A number of immediate corollaries are then derived. 相似文献
4.
Martin Rmoutil 《Czechoslovak Mathematical Journal》2013,63(1):205-217
In the present article we provide an example of two closed non-σ-lower porous sets A,B ? ? such that the product A × B is lower porous. On the other hand, we prove the following: Let X and Y be topologically complete metric spaces, let A ? X be a non-σ-lower porous Suslin set and let B ? Y be a non-σ-porous Suslin set. Then the product A × B is non-σ-lower porous. We also provide a brief summary of some basic properties of lower porosity, including a simple characterization of Suslin non-σ-lower porous sets in topologically complete metric spaces. 相似文献
5.
S. Sánchez-Perales S.V. Djordjevi? 《Journal of Mathematical Analysis and Applications》2011,378(1):289-294
Let X and Y be given Banach spaces. For A∈B(X), B∈B(Y) and C∈B(Y,X), let MC be the operator defined on X⊕Y by . In this paper we give conditions for continuity of τ at MC through continuity of τ at A and B, where τ can be equal to the spectrum or approximate point spectrum. 相似文献
6.
Let X and Y be superreflexive complex Banach spaces and let B(X) and B(Y) be the Banach algebras of all bounded linear operators on X and Y, respectively. If a bijective linear map Φ:B(X)→B(Y) almost preserves the spectra, then it is almost multiplicative or anti-multiplicative. Furthermore, in the case where X=Y is a separable complex Hilbert space, such a map is a small perturbation of an automorphism or an anti-automorphism. 相似文献
7.
Let A and B be Banach function algebras on compact Hausdorff spaces X and Y, respectively, and let $\bar A$ and $\bar B$ be their uniform closures. Let I, I′ be arbitrary non-empty sets, α ∈ ?\{0}, ρ: I → A, τ: l′ → a and S: I → B T: l′ → B be maps such that ρ(I, τ(I′) and S(I), T(I′) are closed under multiplications and contain exp A and expB, respectively. We show that if ‖S(p)T(p′)?α‖Y=‖ρ(p)τ(p′) ? α‖ x for all p ∈ I and p′ ∈ I′, then there exist a real algebra isomorphism S: A → B, a clopen subset K of M B and a homeomorphism ?: M B → M A between the maximal ideal spaces of B and A such that for all f ∈ A, where $\hat \cdot$ denotes the Gelfand transformation. Moreover, S can be extended to a real algebra isomorphism from $\bar A$ onto $\bar B$ inducing a homeomorphism between $M_{\bar B}$ and $M_{\bar A}$ . We also show that under an additional assumption related to the peripheral range, S is complex linear, that is A and B are algebraically isomorphic. We also consider the case where α = 0 and X and Y are locally compact. 相似文献
8.
Fedor Pakovich 《Geometric And Functional Analysis》2016,26(4):1217-1243
We investigate semiconjugate rational functions, that is rational functions A, B related by the functional equation \({A \circ X = X \circ B}\), where X is a rational function. We show that if A and B is a pair of such functions, then either A can be obtained from B by a certain iterative process, or A and B can be described in terms of orbifolds of non-negative Euler characteristic on the Riemann sphere. 相似文献
9.
Let F be a field of arbitrary characteristic, and assume A and B are square matrices, over F, each having a single elementary divisor with associated eigenvalue in F. We express the multiplicities of the elementary divisors of A ? B and A ? I + I ? B in terms of the ranks, over F, of appropriate matrices. 相似文献
10.
Olof J Staffans 《Journal of Differential Equations》1985,58(2):157-191
Consider the abstract linear functional equation (FE) (Dx)(t) = f(t) (t ? 0), x(t) = ?(t) (t ? 0) in a Banach space B. A theorem is proven which contains the following result as a special case. Let Y(R; B; η) be a Lp-space or C0-space on R = (?t8, ∞), with a suitable weight function η, and with values in B. Let D be a closed (unbounded) causal linear operator in Y(R; B; η), which commutes with translations. Suppose that D + λI has a continuous causal inverse for some complex λ, and that D restricted to those functions in Y(R;B;η) which vanish on R? = (?∞, 0] has a continuous causal inverse. Then (FE) generates a strongly continuous semigroup of translation type on a Banach space, which is essentially the cross product of the restriction of the domain of D to R? and Y(R+; B; η). Examples with B = Cn on how the theory applies to a neutral functional differential equation, a difference equation, a Volterra integrodifferential equation (with nonintegrable kernel but integrable resolvent), and a fractional order functional differential equation are given. Also, an abstract neutral functional differential equation in a Hilbert space is studied and applications to an abstract Volterra integrodifferential equation in a Banach space are indicated. 相似文献
11.
12.
M.G. Tkačenko 《Topology and its Applications》1983,15(1):93-98
We consider the question: when is a dense subset of a space XC-embedded in X? We introduce the notion of o-tightness and prove that if each finite subproduct of a product X = Πα?AXα has a countable o-tightness and Y is a subset of X such that πB(Y) = Πα?BXα for every countable B ? A, then Y is C-embedded in X. This result generalizes some of Noble and Ulmer's results on C-embedding. 相似文献
13.
Daniel M Oberlin 《Journal of Functional Analysis》1974,15(4):428-439
Let A be a subspace of C(X), and let K ? X be an interpolation set for A. Let F be a Banach space. We study the following question: When is K a set of interpolation for A ? F, a space of vector-valued functions naturally associated with A ? 相似文献
14.
Richard Bouldin 《Journal of Mathematical Analysis and Applications》1977,61(2):397-403
Let B be a closed linear transformation of the Banach space X into the Banach space Y and let A be a bounded linear transformation of Y into the Banach space Z. A simple condition is shown to be necessary and sufficient for AB to have closed range. Provided B is relatively regular there is a simple necessary and sufficient condition for AB to be relatively regular. Provided B+ and A+ are pseudoinverses for B and A, respectively, the condition that B+A+ is a pseudoinverse for AB is completely characterized. 相似文献
15.
B.P. Duggal 《Journal of Mathematical Analysis and Applications》2009,359(2):631-636
A Banach space operator T∈B(X) satisfies Browder's theorem if the complement of the Weyl spectrum σw(T) of T in σ(T) equals the set of Riesz points of T; T is polaroid if the isolated points of σ(T) are poles (no restriction on rank) of the resolvent of T. Let Φ(T) denote the set of Fredholm points of T. Browder's theorem transfers from A,B∈B(X) to S=LARB (resp., S=A⊗B) if and only if A and B∗ (resp., A and B) have SVEP at points μ∈Φ(A) and ν∈Φ(B) for which λ=μν∉σw(S). If A and B are finitely polaroid, then the polaroid property transfers from A∈B(X) and B∈B(Y) to LARB; again, restricting ourselves to the completion of X⊗Y in the projective topology, if A and B are finitely polaroid, then the polaroid property transfers from A∈B(X) and B∈B(Y) to A⊗B. 相似文献
16.
Y. -K. Song 《Acta Mathematica Hungarica》2007,115(4):315-318
The purpose of this note is to show that there exist two Tychonoff spaces X, Y, a subset A of X and a subset B of Y such that A is weakly almost Lindelöf in X and B is weakly almost Lindelöf in Y, but A × B is not weakly almost Lindelöf in X × Y. 相似文献
17.
Let \((U(t))_ {t\ge 0}\) be a strongly continuous semigroup of bounded linear operators on a Banach space X and B be a bounded operator on X. In this paper, we develop some aspects of the theory of semigroup for which U(t)B (respectively, BU(t), BU(t)B) is demicompact for some (respectively, every) \(t>0\). In addition, we study the demicompactness of similar, subspace and product semigroups. We also investigate the demicompactness of the resolvent. We close this paper by giving some conditions guaranteeing the demicompactness of a generator of a strongly continuous semigroup in a Hilbert space. 相似文献
18.
Let B(X) be the algebra of all bounded linear operators on a complex Banach space X. We give the concrete form of every unital surjective map φ on B(X) such that AB is a non-zero idempotent if and only if φ(A)φ(B) is for all A,B∈B(X) when the dimension of X is at least 3. 相似文献
19.
Yik-Hoi Au-Yeung 《Linear algebra and its applications》1973,7(4):347-350
In this note the author gives a simple proof of the following fact: Let r and s be two positive rational numbers such that r ? s and let A and B be two n × n non-negative definite Hermitian matrices such that Ar ? Br. Then AS ? Bs. 相似文献
20.
Caucher Birkar 《Publications Mathématiques de L'IHéS》2012,115(1):325-368
Let (X/Z,B+A) be a Q-factorial dlt pair where B,A??0 are Q-divisors and K X +B+A?? Q 0/Z. We prove that any LMMP/Z on K X +B with scaling of an ample/Z divisor terminates with a good log minimal model or a Mori fibre space. We show that a more general statement follows from the ACC for lc thresholds. An immediate corollary of these results is that log flips exist for log canonical pairs. 相似文献