共查询到20条相似文献,搜索用时 359 毫秒
1.
Jin Chuan HOU Xiu Ling ZHANG 《数学学报(英文版)》2006,22(1):179-186
Let X be an infinite-dimensional complex Banach space and denote by B(X) the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B(X) onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional ψ on B(X) such that either Φ(T) = cATA^-1 + ψ(T)I for all T, or Φ(T) = cAT*A^-1 + ψ(T)I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite-dimensional Hilbert space, the above similarity invariant additive functional ψ is always zero. 相似文献
2.
Haïkel Skhiri 《Acta Appl Math》2010,112(3):347-356
Let m(T) and q(T) be respectively the minimum and the surjectivity moduli of T∈ℬ(X), where ℬ(X) denotes the algebra of all bounded linear operators on a complex Banach space X. If there exists a semi-invertible but non-invertible operator in ℬ(X) then, given a surjective unital linear map φ: ℬ(X)⟶ℬ(X), we prove that m(T)=m(φ(T)) for all T∈ℬ(X), if and only if, q(T)=q(φ(T)) for all T∈ℬ(X), if and only if, there exists a bijective isometry U∈ℬ(X) such that φ(T)=UTU
−1 for all T∈ℬ(X). 相似文献
3.
Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum σπ (T) of T is defined by σπ (T) = z ∈ σ(T): |z| = maxw∈σ(T) |w|. If surjective (not necessarily linear nor continuous) maps φ, ϕ: A → B satisfy σπ (φ(S)ϕ(T)) = σπ (ST) for all S; T ∈ A, then φ and ϕ are either of the form φ(T) = A
1
TA
2
−1 and ϕ(T) = A
2
TA
1
−1 for some bijective bounded linear operators A
1; A
2 of X onto Y, or of the form φ(T) = B
1
T*B
2
−1 and ϕ(T) = B
2
T*B
−1 for some bijective bounded linear operators B
1;B
2 of X* onto Y.
相似文献
4.
Let T and S be invertible measure preserving transformations of a probability measure space (X, ℬ, μ). We prove that if the group generated by T and S is nilpotent, then exists in L
2-norm for any u, v∈L
∞(X, ℬ, μ). We also show that for A∈ℬ with μ(A)>0 one has . By the way of contrast, we bring examples showing that if measure preserving transformations T, S generate a solvable group, then (i) the above limits do not have to exist; (ii) the double recurrence property fails, that
is, for some A∈ℬ, μ(A)>0, one may have μ(A∩T
-n
A∩S
-
n
A)=0 for all n∈ℕ. Finally, we show that when T and S generate a nilpotent group of class ≤c, in L
2(X) for all u, v∈L
∞(X) if and only if T×S is ergodic on X×X and the group generated by T
-1
S, T
-2
S
2,..., T
-c
S
c
acts ergodically on X.
Oblatum 19-V-2000 & 5-VII-2001?Published online: 12 October 2001 相似文献
5.
Let H be an infinite dimensional complex Hilbert space. Denote by B(H) the algebra of all bounded linear operators on H, and by I(H) the set of all idempotents in B(H). Suppose that Φ is a surjective map from B(H) onto itself. If for every λ ∈ -1,1,2,3, and A, B ∈ B(H),A-λB ∈I(H) ⇔ Φ(A) -λΦ(B) ∈I(H, then Φ is a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that Φ(A) = TAT
-1 for all A ∈ B(H), or Φ(A) = TA*T
-1 for all A ∈ B(H); if, in addition, A-iB ∈I(H)⇔ Φ(A)-iΦ(B) ∈I(H), here i is the imaginary unit, then Φ is either an automorphism or an anti-automorphism. 相似文献
6.
Let p∈(0,1] and s≥[n(1/p−1)], where [n(1/p−1)] denotes the maximal integer no more than n(1/p−1). In this paper, the authors prove that a linear operator T extends to a bounded linear operator from the Hardy space H
p
(ℝ
n
) to some quasi-Banach space ℬ if and only if T maps all (p,2,s)-atoms into uniformly bounded elements of ℬ.
相似文献
7.
8.
Aicke Hinrichs 《Archiv der Mathematik》1997,68(4):265-273
Let A
n
=(a
1,...,a
n) be a system of characters of a compact abelian group A
n
with normalized Haar measure μ and let T be a bounded linear operator from a Banach space X into a Banach space Y. The type norm τ(T|
A
n
) of T with respect to A
n
is the least constant c such that
for all x
1,..., x
n ∈ X. We investigate under which conditions on two systems A
n
and ℬ
n
of characters of compact abelian groups an inequality τ(T|ℬ
n) ≦ τ(T|A
n
) holds for all linear bounded operators T between Banach spaces. It turns out that this can be tested on a certain operator depending only on the system ℬ
n. Moreover, it is equivalent to strong algebraic relations between A
n
and ℬ
n as well as to relations between its distributions. In particular, for systems of trigonometric functions this inequality
for all linear bounded operators even implies equality for all linear bounded operators.
The author is supported by DFG grant PI 322/1-1. The content of this paper is part of the authors PhD-thesis written under
the supervision of A. Pietsch. 相似文献
9.
Let H be a Hilbert space and A be a standard *-subalgebra of B(H). We show that a bijective map Ф : A →A preserves the Lie-skew product AB - BA* if and only if there is a unitary or conjugate unitary operator U ∈A(H) such that Ф(A) = UAU* for all A ∈ A, that is, Фis a linear * -isomorphism or a conjugate linear *-isomorphism. 相似文献
10.
Let L(H) denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space H into itself. Given A ∈ L(H), we define the elementary operator Δ
A
: L(H) → L(H) by Δ
A
(X) = AXA − X. In this paper we study the class of operators A ∈ L(H) which have the following property: ATA = T implies AT*A = T* for all trace class operators T ∈ C
1(H). Such operators are termed generalized quasi-adjoints. The main result is the equivalence between this character and the
fact that the ultraweak closure of the range of Δ
A
is closed under taking adjoints. We give a characterization and some basic results concerning generalized quasi-adjoints
operators. 相似文献
11.
Kirsti Mattila 《Israel Journal of Mathematics》1980,37(1-2):164-170
For some normal operators (T=H+iK) on a Banach spaceX we study the dual space of the Banach algebraA (H, K) assuming thatX* is weakly complete and we study the decompositionX=Ker (T) ⊕ (TX)− for spacesX ⊅c
0. 相似文献
12.
LU Chuanrong QIU Jin & XU Jianjun School of Mathematics Statistics Zhejiang University of Finance Economics Hangzhou China Department of Mathematics Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2006,49(12):1788-1799
Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn Rn, where supn E|Rn| <∞and Rn = o(n~(1/2)) a.s., or Rn = O(n1/2-2γ) a.s., 0 <γ< 1/8. In this paper, we prove the almost sure central limit theorem (ASCLT) and the function-typed almost sure central limit theorem (FASCLT) for the random function Tn. As a consequence, it can be shown that ASCLT and FASCLT also hold for U-statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc. 相似文献
13.
Let X be a compact metric space and let Lip(X) be the Banach algebra of all scalar- valued Lipschitz functions on X, endowed with a natural norm. For each f ∈ Lip(X), σπ(f) denotes the peripheral spectrum of f. We state that any map Φ from Lip(X) onto Lip(Y) which preserves multiplicatively the peripheral spectrum:
σπ(Φ(f)Φ(g)) = σπ(fg), A↓f, g ∈ Lip(X)
is a weighted composition operator of the form Φ(f) = τ· (f °φ) for all f ∈ Lip(X), where τ : Y → {-1, 1} is a Lipschitz function and φ : Y→ X is a Lipschitz homeomorphism. As a consequence of this result, any multiplicatively spectrum-preserving surjective map between Lip(X)-algebras is of the form above. 相似文献
σπ(Φ(f)Φ(g)) = σπ(fg), A↓f, g ∈ Lip(X)
is a weighted composition operator of the form Φ(f) = τ· (f °φ) for all f ∈ Lip(X), where τ : Y → {-1, 1} is a Lipschitz function and φ : Y→ X is a Lipschitz homeomorphism. As a consequence of this result, any multiplicatively spectrum-preserving surjective map between Lip(X)-algebras is of the form above. 相似文献
14.
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
15.
We show that T is a surjective multiplicative (but not necessarily linear) isometry from the Smirnov class on the open unit disk, the ball, or the polydisk onto itself,
if and only if there exists a holomorphic automorphism Φ such that T(f)=f ○ Φ for every class element f or T(f) = [`(f° [`(j)] )]\overline {f^\circ \bar \varphi } for every class element f, where the automorphism Φ is a unitary transformation in the case of the ball and Φ(z
1, ..., z
n
) = (l1 zi1 ,...,ln zin )(\lambda _1 z_{i_1 } ,...,\lambda _n z_{i_n } ) for |λ
j
| = 1, 1 ≤ j ≤ n, and (i
1; ..., i
n
)is some permutation of the integers from 1through n in the case of the n-dimensional polydisk. 相似文献
16.
Spaces of analytic functions of Hardy-Bloch type 总被引:1,自引:1,他引:0
For 0<p≤∞ and 0<q≤∞, the space of Hardy-Bloch type ℬ(p,q) consists of those functionsf which are analytic in the unit diskD such that (1−r)M
p
(r,f′)⊂L
q
(dr/(1−r)). We note that ℬ(∞,∞) coincides with the Bloch space ℬ and that ℬ⊂ℬ(p,∞) for allp. Also, the space ℬ(p,p) is the Dirichlet spaceD
p−1
p
.
We prove a number of results on decomposition of spaces with logarithmic weights which allow us to obtain sharp results about
the mean growth of the ℬ(p,q). In particular, we prove that iff is an analytic function inD and 2≤p<∞, then the conditionM
p
(r,f′)=O((1−r)−1), asr→1, implies that
. This result is an improvement of the well-known estimate of Clunie and MacGregor and Makarov about the integral means of
Bloch functions, and it also improves the main result in a recent paper by Girela and Peláez. We also consider the question
of characterizing the univalent functions in the spaces ℬ(p,2), 0<p<∞, and in some other related spaces and give some applications of our estimates to study the Carleson measures for the spaces
ℬ(p,2) andD
p−1
p
.
The first and third authors were supported by grants from “E1 Ministerio de Educación y Ciencia”, Spain (MTN2004-00078 and
MTN2004-21420-E) and by a grant from “La Junta de Andalucía” (FQM-210).
The second author was supported in part by MNZŽS Grant, No. ON144010, Serbia. 相似文献
17.
Two invertible dynamical systems (X, gA, μ, T) and (Y, ℬ, ν, S), where X, Y are metrizable spaces and T, S are homeomorphisms on X and Y, are said to be finitarily orbit equivalent if there exists an invertible measure preserving mapping ϕ from a subset X
0 of X of full measure to a subset Y
0 of Y of full measure such that ϕ|x
0 is continuous in the relative topology on X
0, ϕ
−1|Y
0 is continuous in the relative topology on Y
0 and ϕ(Orb
T
(x)) = Orb
Sϕ
(x) for μ-a.e. x ∈ X. In this article a finitary orbit equivalence mapping is shown to exist between any two irreducible Markov chains. 相似文献
18.
Let X and Y be two infinite dimensional real or complex Banach spaces, and let φ: ?(X)?→??(Y) be an additive surjective mapping that preserves semi-Fredholm operators in both directions. In the complex Hilbert space context, Mbekhta and ?emrl [M. Mbekhta and P. ?emrl, Linear maps preserving semi-Fredholm operators and generalized invertibility, Linear Multilinear Algebra 57 (2009), pp. 55–64] determined the structure of the induced map on the Calkin algebra. In this article, we show the following: given an integer n?≥?1, if φ preserves in both directions ? n (X) (resp., 𝒬 n (X)), the set of semi-Fredholm operators on X of non-positive (resp., non-negative) index, having dimension of the kernel (resp., codimension of the range) less than n, then φ(T)?=?UTV for all T or φ(T)?=?UT*V for all T, where U and V are two bijective bounded linear, or conjugate linear, mappings between suitable spaces. 相似文献
19.
M. Zippin 《Israel Journal of Mathematics》1981,39(4):349-358
It is proved that there exists a positive function Φ(∈) defined for sufficiently small ∈ 〉 0 and satisfying limt→0 Φ(∈) =0 such that for any integersn 〉>0, ifQ is a projection ofl
1
n
onto ak-dimensional subspaceE with ‖|Q‖|≦1+∈ then there is an integerh〉=k(1−Φ(∈)) and anh-dimensional subspaceF ofE withd(F,l
1
h
) 〈= 1+Φ (∈) whered(X, Y) denotes the Banach-Mazur distance between the Banach spacesX andY. Moreover, there is a projectionP ofl
1
n
ontoF with ‖|P‖| ≦1+Φ(∈).
Author was partially supported by the N.S.F. Grant MCS 79-03042. 相似文献
20.
Vidmantas Bentkus 《Israel Journal of Mathematics》2007,158(1):1-17
Let M
n
= X
1 + ⋯ + X
n
be a martingale with bounded differences X
m
= M
m
− M
m
−1 such that ℙ{a
m
− σ
m
≤ X
m
≤ a
m
+ σ
m
} = 1 with nonrandom nonnegative σ
m
and σ(X
1, …, X
m
−1)-measurable random variables a
m
. Write σ
2 = σ
1
2
+ ⋯ + σ
n
2
. Let I(x) = 1 − Φ(x), where Φ is the standard normal distribution function. We prove the inequalities
with a constant c such that 3.74 … ≤ c ≤ 7.83 …. The result yields sharp bounds in some models related to the measure concentration. In the case where all a
m
= 0 (or a
m
≤ 0), the bounds for constants improve to 3.17 … ≤ c ≤ 4.003 …. The inequalities are new even for independent X
1, …, X
n
, as well as for linear combinations of independent Rademacher random variables.
Research supported by Max Planck Institute for Mathematics, Bonn 相似文献