共查询到20条相似文献,搜索用时 62 毫秒
1.
B. P. Duggal 《Integral Equations and Operator Theory》2009,63(1):17-28
A Banach space operator T ∈ B(χ) is polaroid if points λ ∈ iso σ(T) are poles of the resolvent of T. Let denote, respectively, the approximate point, the Weyl, the Weyl essential approximate, the upper semi–Fredholm and lower
semi–Fredholm spectrum of T. For A, B and C ∈ B(χ), let M
C
denote the operator matrix . If A is polaroid on , M
0 satisfies Weyl’s theorem, and A and B satisfy either of the hypotheses (i) A has SVEP at points and B has SVEP at points , or, (ii) both A and A* have SVEP at points , or, (iii) A* has SVEP at points and B
* has SVEP at points , then . Here the hypothesis that λ ∈ π0(M
C
) are poles of the resolvent of A can not be replaced by the hypothesis are poles of the resolvent of A.
For an operator , let . We prove that if A* and B* have SVEP, A is polaroid on π
a
0(M
C) and B is polaroid on π
a
0(B), then .
相似文献
2.
F. M. Al-Oboudi 《Complex Analysis and Operator Theory》2011,5(3):647-658
Let A denote the class of analytic functions f, in the open unit disk E = {z : |z| < 1}, normalized by f(0) = f′(0) − 1 = 0. In this paper, we introduce and study the class STn,al,m(h){ST^{n,\alpha}_{\lambda,m}(h)} of functions f ? A{f\in A}, with
\fracDn,al fm(z)z 1 0{\frac{D^{n,\alpha}_\lambda f_m(z)}{z}\neq 0}, satisfying
\fracz(Dn,al f(z))¢Dn,al fm(z)\prec h(z), z ? E,\frac{z\left(D^{n,\alpha}_\lambda f(z)\right)'}{D^{n,\alpha}_\lambda f_m(z)}\prec h(z),\quad z\in E, 相似文献
3.
LetX andY denote two complex Banach spaces and letB(Y, X) denote the algebra of all bounded linear operators fromY toX. ForA∈B(X)
n
,B∈B(Y)
n
, the elementary operator acting onB(Y, X) is defined by
. In this paper we obtain the formulae of the spectrum and the essential spectrum of Δ(A, B) by using spectral mapping theorems. Forn=1, we prove thatS
p
(L
A
,R
B
)=σ(A)×σ(B) and
. 相似文献
4.
J. Hu 《Transformation Groups》2010,15(2):333-370
Let V be a 2m-dimensional symplectic vector space over an algebraically closed field K. Let $ \mathfrak{B}_n^{(f)} | / | \vphantom V ?n V ?n V ?n\mathfrakBn(f) ) {\text{En}}{{\text{d}}_{K{\text{Sp}}(V)}}\left( {{{{V^{ \otimes n}}} \mathord{\left/{\vphantom {{{V^{ \otimes n}}} {{V^{ \otimes n}}}}} \right.} {{V^{ \otimes n}}}}\mathfrak{B}_n^{(f)}} \right) are both independent of K, and the natural homomorphism from \mathfrakBn( - 2m ) \mathord | / | \vphantom ( - 2m ) \mathfrakBn(f) \mathfrakBn(f) {\mathfrak{B}_n}{{\left( { - 2m} \right)} \mathord{\left/{\vphantom {{\left( { - 2m} \right)} {\mathfrak{B}_n^{(f)}}}} \right.} {\mathfrak{B}_n^{(f)}}} to \textEn\textdK\textSp(V)( V ?n \mathord | / | \vphantom V ?n V ?n V ?n\mathfrakBn(f) ) {\text{En}}{{\text{d}}_{K{\text{Sp}}(V)}}\left( {{{{V^{ \otimes n}}} \mathord{\left/{\vphantom {{{V^{ \otimes n}}} {{V^{ \otimes n}}}}} \right.} {{V^{ \otimes n}}}}\mathfrak{B}_n^{(f)}} \right) is always surjective. We show that HTf ?n \mathcal{H}\mathcal{T}_f^{ \otimes n} has a Weyl filtration and is isomorphic to the dual of V ?n\mathfrakBn(f) \mathord | / | \vphantom V ?n\mathfrakBn(f) V V ?n\mathfrakBn( f + 1 ) {{{{V^{ \otimes n}}\mathfrak{B}_n^{(f)}} \mathord{\left/{\vphantom {{{V^{ \otimes n}}\mathfrak{B}_n^{(f)}} V}} \right.} V}^{ \otimes n}}\mathfrak{B}_n^{\left( {f + 1} \right)} as an \textSp(V) - ( \mathfrakBn( - 2m ) \mathord | / |
\vphantom ( - 2m ) \mathfrakBn( f + 1 ) \mathfrakBn( f + 1 ) ) {\text{Sp}}(V) - \left( {{\mathfrak{B}_n}{{\left( { - 2m} \right)} \mathord{\left/{\vphantom {{\left( { - 2m} \right)} {\mathfrak{B}_n^{\left( {f + 1} \right)}}}} \right.} {\mathfrak{B}_n^{\left( {f + 1} \right)}}}} \right) -bimodule. We obtain an
\textSp(V) - \mathfrakBn {\text{Sp}}(V) - {\mathfrak{B}_n} -bimodules filtration of V
⊗n
such that each successive quotient is isomorphic to some
?( l) ?zg,l\mathfrakBn \nabla \left( \lambda \right) \otimes {z_{g,\lambda }}{\mathfrak{B}_n} with λ ⊢ n 2g, ℓ(λ)≤m and 0 ≤ g ≤ [n/2], where ∇(λ) is the co-Weyl module associated to λ and z
g,λ is an explicitly constructed maximal vector of weight λ. As a byproduct, we show that each right
\mathfrakBn {\mathfrak{B}_n} -module
zg,l\mathfrakBn {z_{g,\lambda }}{\mathfrak{B}_n} is integrally defined and stable under base change. 相似文献
5.
James R. Holub 《Israel Journal of Mathematics》1985,52(3):231-238
LetW(D) denote the set of functionsf(z)=Σ
n=0
∞
A
n
Z
n
a
nzn for which Σn=0
∞|a
n
|<+∞. Given any finite set lcub;f
i
(z)rcub;
i=1
n
inW(D) the following are equivalent: (i) The generalized shift sequence lcub;f
1(z)z
kn
,f
2(z)z
kn+1, …,f
n
(z)z
(k+1)n−1rcub;
k=0
∞
is a basis forW(D) which is equivalent to the basis lcub;z
m
rcub;
m=0
∞
. (ii) The generalized shift sequence is complete inW(D), (iii) The function
has no zero in |z|≦1, wherew=e
2πiti
/n. 相似文献
6.
Rumi Shindo 《Mediterranean Journal of Mathematics》2011,8(1):81-95
Let A, B be uniform algebras. Suppose that A
0, B
0 are subgroups of A
−1, B
−1 that contain exp A, exp B respectively. Let α be a non-zero complex number. Suppose that m, n are non-zero integers and d is the greatest common divisor of m and n. If T : A
0 → B
0 is a surjection with ||T(f)mT(g)n - a||¥ = ||fmgn - a||¥{\|T(f)^{m}T(g)^{n} - \alpha\|_{\infty} = \|f^{m}g^{n} - \alpha\|_{\infty}} for all f,g ? A0{f,g \in A_0}, then there exists a real-algebra isomorphism [(T)\tilde] : A ? B{\tilde{T} : A \rightarrow B} such that [(T)\tilde](f)d = (T(f)/T(1))d{\tilde{T}(f)^d = (T(f)/T(1))^d} for every f ? A0{f \in A_0}. This result leads to the following assertion: Suppose that S
A
, S
B
are subsets of A, B that contain A
−1, B
−1 respectively. If m, n > 0 and a surjection T : S
A
→ S
B
satisfies ||T(f)mT(g)n - a||¥ = ||fmgn - a||¥{\|T(f)^{m}T(g)^{n} - \alpha\|_{\infty} = \|f^{m}g^{n} - \alpha\|_{\infty}} for all f, g ? SA{f, g \in S_A}, then there exists a real-algebra isomorphism [(T)\tilde] : A ? B{\tilde{T} : A \rightarrow B} such that [(T)\tilde](f)d = (T(f)/T(1))d{\tilde{T}(f)^d = (T(f)/T(1))^d} for every f ? SA{f \in S_A}. Note that in these results and elsewhere in this paper we do not assume that T(exp A) = exp B. 相似文献
7.
Takuro Fukunaga 《Graphs and Combinatorics》2011,27(5):647-659
An undirected graph G = (V, E) is called
\mathbbZ3{\mathbb{Z}_3}-connected if for all
b: V ? \mathbbZ3{b: V \rightarrow \mathbb{Z}_3} with ?v ? Vb(v)=0{\sum_{v \in V}b(v)=0}, an orientation D = (V, A) of G has a
\mathbbZ3{\mathbb{Z}_3}-valued nowhere-zero flow
f: A? \mathbbZ3-{0}{f: A\rightarrow \mathbb{Z}_3-\{0\}} such that ?e ? d+(v)f(e)-?e ? d-(v)f(e)=b(v){\sum_{e \in \delta^+(v)}f(e)-\sum_{e \in \delta^-(v)}f(e)=b(v)} for all v ? V{v \in V}. We show that all 4-edge-connected HHD-free graphs are
\mathbbZ3{\mathbb{Z}_3}-connected. This extends the result due to Lai (Graphs Comb 16:165–176, 2000), which proves the
\mathbbZ3{\mathbb{Z}_3}-connectivity for 4-edge-connected chordal graphs. 相似文献
8.
Lou Yuanren 《分析论及其应用》1990,6(1):46-64
Let f∈Ap. For any positive integer l, the quantity Δ1,n−1(f:z) has been studied extensively. Here we give some quantitative estimates for
and investigate some pointwise estimates of Δ
l,n−1
(r)
(f;z).
Supported by National Science Foundation of China 相似文献
9.
Salah Mecheri 《Integral Equations and Operator Theory》2005,53(3):403-409
Let B(H) denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space H into itself. Let A = (A1,A2,.., An) and B = (B1, B2,.., Bn) be n-tuples in B(H), we define the elementary operator
by
In this paper we initiate the study of some properties of the range of such operators. 相似文献
10.
LiPing Huang 《中国科学A辑(英文版)》2009,52(11):2404-2418
Let D be a division ring with an involution-,H2(D) be the set of 2 × 2 Hermitian matrices over D. Let ad(A,B) = rank(A-B) be the arithmetic distance between A,B ∈ H2(D) . In this paper,the fundamental theorem of the geometry of 2 × 2 Hermitian matrices over D(char(D) = 2) is proved:if :H2(D) → H2(D) is the adjacency preserving bijective map,then is of the form (X) = tP XσP +(0) ,where P ∈ GL2(D) ,σ is a quasi-automorphism of D. The quasi-automorphism of D is studied,and further results are obtained. 相似文献
11.
Heinz Langer Alexander Markus Vladimir Matsaev 《Integral Equations and Operator Theory》2009,63(4):533-545
In this note we continue the study of spectral properties of a self-adjoint analytic operator function A(z) that was started in [5]. It is shown that if A(z) satisfies the Virozub–Matsaev condition on some interval Δ0 and is boundedly invertible in the endpoints of Δ0, then the ‘embedding’ of the original Hilbert space into the Hilbert space , where the linearization of A(z) acts, is in fact an isomorphism between a subspace of and . As a consequence, properties of the local spectral function of A(z) on Δ0 and a so-called inner linearization of the operator function A(z) in the subspace are established.
相似文献
12.
We consider the Schr?dinger operator Hγ = ( − Δ)l + γ V(x)· acting in the space
$$L_2 (\mathbb{R}^d ),$$ where 2l ≥ d, V (x) ≥ 0, V (x) is continuous and is not identically zero, and
$$\lim _{|{\mathbf{x}}| \to \infty } V({\mathbf{x}}) = 0.$$ We obtain an asymptotic expansion as
$$\gamma \uparrow 0$$of the bottom negative eigenvalue of Hγ, which is born at the moment γ = 0 from the lower bound λ = 0 of the spectrum σ(H0) of the unperturbed operator H0 = ( − Δ)l (a virtual eigenvalue). To this end we develop a supplement to the Birman-Schwinger theory on the process of the birth of
eigenvalues in the gap of the spectrum of the unperturbed operator H0. Furthermore, we extract a finite-rank portion Φ(λ) from the Birman- Schwinger operator
$$X_V (\lambda ) = V^{\frac{1} {2}} R_\lambda (H_0 )V^{\frac{1}{2}} ,$$ which yields the leading terms for the desired asymptotic
expansion. 相似文献
13.
Victor I. Lomonosov Heydar Radjavi Vladimir G. Troitsky 《Integral Equations and Operator Theory》2008,60(3):405-418
An algebra of operators on a Banach space X is said to be transitive if X has no nontrivial closed subspaces invariant under every member of the algebra. In this paper we investigate a number of
conditions which guarantee that a transitive algebra of operators is “large” in various senses. Among these are the conditions
of algebras being localizing or sesquitransitive. An algebra is localizing if there exists a closed ball B ∌ 0 such that for every sequence (x
n
) in B there exists a subsequence and a bounded sequence (A
k
) in the algebra such that converges to a non-zero vector. An algebra is sesquitransitive if for every non-zero z ∈ X there exists C > 0 such that for every x linearly independent of z, for every non-zero y ∈ X, and every there exists A in the algebra such that and ||Az|| ≤ C||z||. We give an algebraic version of this definition as well, and extend Jacobson’s density theorem to algebraically sesquitransitive
rings.
The second and the third authors were supported by NSERC. 相似文献
14.
Let ${\mathcal {H}_{1}}
15.
In this paper we derive a technique for obtaining limit theorems for suprema of Lévy processes from their random walk counterparts. For each a>0, let $\{Y^{(a)}_{n}:n\ge1\}
16.
N. N. Rogovtsov 《Differential Equations》2008,44(9):1249-1268
We carry out a qualitative analysis and suggest a method for the solution of the two-point boundary value problems A l υ = g, x ? [0, l], l ? (0, L) = B ? R +; $$ \alpha v'_x \left| {_{x = + 0} = F_1 (v,l)} \right|_{x = 0} , \beta v'_x \left| {_{x = l - 0} = F_2 (v,l)} \right|_{x = l} , $$ , where α, β ? R, υ is the unknown function, g = g(x) is a given real function, F 1(y, l) and F 2(y, l) are known real functions defined on the sets Y 1 × B and Y 2 × B, respectively, where Y 1 ∪ Y 2 ? R, and A l is the restriction of A corresponding to the embedding parameter l. (Here A is an operator taking an arbitrary function in the set of function classes defined in the paper to C(B 1), where B 1 = [0, L).) The study takes into account the dependence of solutions of various versions of these two-point boundary value problems on the parameter l. We construct algorithms for the reduction of these families of two-point boundary value problems to Cauchy problems for ordinary differential equations and integro-differential equations that contain only first derivatives of the unknown functions with respect to the parameter l. 相似文献
17.
For α satisfying 0 < α < π, suppose that C
1 and C
2 are rays from the origin, C
1: z = re
i(π−α) and C
2: z = re
i(π+α), r ≥ 0, and that D = {z: | arg z − π| < α}. Let u be a nonconstant subharmonic function in the plane and define B(r, u) = sup|z|=r
u(z) and A
D
(r, u) = $
\inf _{z \in \bar D_r }
$
\inf _{z \in \bar D_r }
u(z), where D
r
= {z: z ∈ D and |z| = r}. If u(z) = (1 + o(1))B(|z|, u) as z → ∞ on C
1 ∪ C
2 and A
D
(r, u) = o(B(r, u)) as r → ∞, then the lower order of u is at least π/(2α). 相似文献
18.
We study functions f(z) holomorphic in having the property f(z) ≠ 0 for 0 < Im z < 1 and we obtain lower bounds for |f(z)| for 0 < Im z < 1. In our analysis we deal with scalar functions f(z) as well as with operator valued holomorphic functions I + A(z) assuming that A(z) is a trace class operator for and I + A(z) is invertible for 0 < Im z < 1 and is unitary for .
A. Borichev was partially supported by the ANR project DYNOP. 相似文献
19.
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
20.
S. Mecheri 《Czechoslovak Mathematical Journal》2007,57(2):697-703
Let ℋ be a separable infinite dimensional complex Hilbert space, and let ℒ(H) denote the algebra of all bounded linear operators on ℋ into itself. Let A = (A
1, A
2,..., A
n), B = (B
1, B
2,..., B
n) be n-tuples of operators in ℒ(H); we define the elementary operators Δ
A,B
: ℒ(H) ↦ ℒ(H) by
|