共查询到20条相似文献,搜索用时 52 毫秒
1.
Constantin Costara 《Integral Equations and Operator Theory》2012,73(1):7-16
Let X be a complex Banach space and let B(X){\mathcal{B}(X)} be the space of all bounded linear operators on X. For x ? X{x \in X} and T ? B(X){T \in \mathcal{B}(X)}, let rT(x) = limsupn ? ¥ || Tnx|| 1/n{r_{T}(x) =\limsup_{n \rightarrow \infty} \| T^{n}x\| ^{1/n}} denote the local spectral radius of T at x. We prove that if j: B(X) ? B(X){\varphi : \mathcal{B}(X) \rightarrow \mathcal{B}(X)} is linear and surjective such that for every x ? X{x \in X} we have r
T
(x) = 0 if and only if rj(T)(x) = 0{r_{\varphi(T)}(x) = 0}, there exists then a nonzero complex number c such that j(T) = cT{\varphi(T) = cT} for all T ? B(X){T \in \mathcal{B}(X) }. We also prove that if Y is a complex Banach space and j:B(X) ? B(Y){\varphi :\mathcal{B}(X) \rightarrow \mathcal{B}(Y)} is linear and invertible for which there exists B ? B(Y, X){B \in \mathcal{B}(Y, X)} such that for y ? Y{y \in Y} we have r
T
(By) = 0 if and only if rj( T) (y)=0{ r_{\varphi ( T) }(y)=0}, then B is invertible and there exists a nonzero complex number c such that j(T) = cB-1TB{\varphi(T) =cB^{-1}TB} for all T ? B(X){T \in \mathcal{B}(X)}. 相似文献
2.
Mikhail Gromov 《Geometric And Functional Analysis》2009,19(3):743-841
We find lower bounds on the topological complexity of the critical (values) sets S(F) ì Y{\Sigma(F) \subset Y} of generic smooth maps F : X → Y, as well as on the complexity of the fibers F-1(y) ì X{F^{-1}(y) \subset X} in terms of the topology of X and Y, where the relevant topological invariants of X are often encoded in the geometry of some Riemannian metric supported by X. 相似文献
3.
Daniela Roşu 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(4):479-496
In this paper we consider a nonlinear evolution reaction–diffusion system governed by multi-valued perturbations of m-dissipative operators, generators of nonlinear semigroups of contractions. Let X and Y be real Banach spaces, ${\mathcal{K}}In this paper we consider a nonlinear evolution reaction–diffusion system governed by multi-valued perturbations of m-dissipative operators, generators of nonlinear semigroups of contractions. Let X and Y be real Banach spaces, K{\mathcal{K}} be a nonempty and locally closed subset in
\mathbbR ×X×Y, A:D(A) í X\rightsquigarrow X, B:D(B) í Y\rightsquigarrow Y{\mathbb{R} \times X\times Y,\, A:D(A)\subseteq X\rightsquigarrow X, B:D(B)\subseteq Y\rightsquigarrow Y} two m-dissipative operators, F:K ? X{F:\mathcal{K} \rightarrow X} a continuous function and
G:K \rightsquigarrow Y{G:\mathcal{K} \rightsquigarrow Y} a nonempty, convex and closed valued, strongly-weakly upper semi-continuous (u.s.c.) multi-function. We prove a necessary
and a sufficient condition in order that for each (t,x,h) ? K{(\tau,\xi,\eta)\in \mathcal{K}}, the next system
{ lc u¢(t) ? Au(t)+F(t,u(t),v(t)) t 3 tv¢(t) ? Bv(t)+G(t,u(t),v(t)) t 3 tu(t)=x, v(t)=h, \left\{ \begin{array}{lc} u'(t)\in Au(t)+F(t,u(t),v(t))\quad t\geq\tau \\ v'(t)\in Bv(t)+G(t,u(t),v(t))\quad t\geq\tau \\ u(\tau)=\xi,\quad v(\tau)=\eta, \end{array} \right. 相似文献
4.
R. Thangadurai 《Archiv der Mathematik》2002,78(5):386-396
A polynomial P(X) with coefficients {ǃ} of odd degree N - 1 is cyclotomic if and only if¶¶P(X) = ±Fp1 (±X)Fp2(±Xp1) ?Fpr(±Xp1 p2 ?pr-1) P(X) = \pm \Phi_{p1} (\pm X)\Phi_{p2}(\pm X^{p1}) \cdots \Phi_{p_r}(\pm X^{p1 p2 \cdots p_r-1}) ¶where N = p1 p2 · · · pr and the pi are primes, not necessarily distinct, and where Fp(X) : = (Xp - 1) / (X - 1) \Phi_{p}(X) := (X^{p} - 1) / (X - 1) is the p-th cyclotomic polynomial. This is a conjecture of Borwein and Choi [1]. We prove this conjecture for a class of polynomials of degree N - 1 = 2r pl - 1 N - 1 = 2^{r} p^{\ell} - 1 for any odd prime p and for integers r, l\geqq 1 r, \ell \geqq 1 . 相似文献
5.
Soit _boxclose{\mathcal V} un anneau de valuation discrète complet d’inégales caractéristiques (0, p), de corps résiduel parfait k, de corps des fractions K. Soient X une variété sur k, Y un ouvert de X. Nous prolongeons le théorème de pleine fidélité de Kedlaya de la manière suivante (en effet, nous ne supposons pas Y lisse): le foncteur canonique
F\text-Isoc f (Y,X/K) ? F\text-Isoc f (Y,Y/K) {F\text{-}\mathrm{Isoc} ^{\dag} (Y,X/K) \to F\text{-}\mathrm{Isoc} ^{\dag} (Y,Y/K) } est pleinement fidèle. Supposons à présent Y lisse. Nous construisons la catégorie Isoc ff (Y,X/K){\mathrm{Isoc} ^{\dag\dag} (Y,X/K) } des isocristaux partiellement surcohérents sur (Y, X) dont les objets sont certains D{\mathcal D} -modules arithmétiques. De plus, nous vérifions l’équivalence de catégories sp (Y,X),+: Isoc f (Y,X/K) @ Isoc ff (Y,X/K){{\rm sp} _{(Y,X),+}: \mathrm{Isoc} ^{\dag} (Y,X/K) \cong \mathrm{Isoc} ^{\dag\dag} (Y,X/K)} . 相似文献
6.
Real hypersurfaces of a complex manifold admit a naturally induced almost contact structure F′ from the almost complex structure of the ambient manifold. We prove that for any F′-invariant submanifold M of a geodesic hypersphere in a non-flat complex space form and of a horosphere in a complex hyperbolic space, its second
fundamental form h satisfies the condition h(FX,Y ) - h(X, FY) = g(FX, Y )h, X,Y ? T(M), 0 1 h ? T^(M){h(FX,Y ) - h(X, FY) = g(FX, Y )\eta, X,Y \in T(M), 0 \ne \eta \in {T^\perp}(M)}, which has been considered in [2] and [3]. 相似文献
7.
Recently, Blecher and Kashyap have generalized the notion of W
*-modules over von Neumann algebras to the setting where the operator algebras are σ closed algebras of operators on a Hilbert space. They call these modules weak* rigged modules. We characterize the weak* rigged modules over nest algebras. We prove that Y is a right weak* rigged module over a nest algebra Alg(M){\rm{Alg}(\mathcal M)} if and only if there exists a completely isometric normal representation F{\Phi } of Y and a nest algebra Alg(N){\rm{Alg}(\mathcal N)} such that Alg(N) F(Y)Alg(M) ì F(Y){\rm{Alg}(\mathcal N) \Phi (Y)\rm{Alg}(\mathcal M)\subset \Phi (Y)} while F(Y){\Phi (Y)} is implemented by a continuous nest homomorphism from M{\mathcal M} onto N{\mathcal N} . We describe some properties which are preserved by continuous CSL homomorphisms. 相似文献
8.
B. Taeri 《Archiv der Mathematik》2001,77(6):456-460
Let n be an integer and Bn \mathcal B_n be the variety defined by the law [xn,y][x,yn]-1 = 1.¶ Let Bn* \mathcal B_n^* be the class of groups in which for any infinite subsets X, Y there exist x ? X x \in X and y ? Y y \in Y such that [xn,y][x,yn]-1 = 1. For $ n \in {\pm 2, 3\} $ n \in {\pm 2, 3\} we prove that¶ Bn* = Bn èF \mathcal B_n^* = \mathcal B_n \cup \mathcal F , F \mathcal F being the class of finite groups. Also for $ n \in {- 3, 4\} $ n \in {- 3, 4\} and an infinite group G which has finitely many elements of order 2 or 3 we prove that G ? Bn* G \in \mathcal B_n^* if and only if G ? Bn G \in \mathcal B_n . 相似文献
9.
We introduce the notion of compactly locally reflexive Banach spaces and show that a Banach space X is compactly locally reflexive if and only if for all reflexive Banach spaces Y. We show that X
* has the approximation property if and only if X has the approximation property and is compactly locally reflexive. The weak metric approximation property was recently introduced
by Lima and Oja. We study two natural weak compact versions of this property. If X is compactly locally reflexive then these two properties coincide. We also show how these properties are related to the compact
approximation property and the compact approximation property with conjugate operators for dual spaces. 相似文献
10.
The main result is that, for any projective compact analytic subset Y of dimension q > 0 in a reduced complex space X, there is a neighborhood Ω of Y such that, for any covering space ${\Upsilon\colon\widehat X\to X}
11.
Liming Wu 《Journal of Theoretical Probability》2009,22(4):983-991
A beautiful result of Sarmanov (Dokl. Akad. Nauk SSSR 121(1), 52–55, 1958) says that for a Gaussian vector (X,Y),
\operatorname Var(\mathbb E[f(Y)|X]) £ r2\operatorname Var(f(Y))\operatorname {Var}(\mathbb {E}[f(Y)|X])\le \rho^{2}\operatorname {Var}(f(Y))
for all measurable functions f, where ρ is the (linear) correlation coefficient between X and Y. We generalize this result to a general Φ-entropy (a nonlinear version of his result) by means of a previous result of D. Chafai based on Bakry–Emery’s Γ
2-technique and tensorization. 相似文献
12.
We give the general and the so-called density function solutions of equation
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