共查询到20条相似文献,搜索用时 11 毫秒
1.
Bruce A. Barnes 《Proceedings of the American Mathematical Society》2005,133(1):155-162
In this paper, relationships among the concepts, majorization, range inclusion, and factorization, are studied in a general setting for bounded linear operators. Some applications of these concepts are given.
2.
Daniel H. Luecking 《Proceedings of the American Mathematical Society》2000,128(4):1109-1116
For composition operators on spaces of analytic functions it is well known that norm estimates can be converted to Carleson measure estimates. The boundedness of the composition operator becomes equivalent to a Carleson measure inequality. The measure corresponding to a composition operator on the Dirichet space is , where is the cardinality of the preimage . The composition operator will have closed range if and only if the corresponding measure satisfies a ``reverse Carleson measure' theorem: for all . Assuming is bounded, a necessary condition for this inequality is a reverse of the Carleson condition: (C) for all Carleson squares . It has long been known that this is not sufficient for a completely general measure. Here we show that it is also not sufficient for the special measures . That is, we construct a function such that is bounded and satisfies (C) but the composition operator does not have closed range.
3.
We deal with the space consisting of those analytic functions on the unit disc such that , with . We determine the critical rate of decay of such that the pointwise multiplication operator , and analytic, has closed range in only in the trivial case that is the product of an invertible function in and a finite Blaschke product.
4.
Bruce A. Barnes 《Proceedings of the American Mathematical Society》1998,126(4):1055-1061
Let and be bounded linear operators defined on Banach spaces, , . When , then the operators and have many basic operator properties in common. This situation is studied in this paper.
5.
By the well-known result of Brown, Chevreau and Pearcy, every Hilbert space contraction with spectrum containing the unit circle has a nontrivial closed invariant subspace. Equivalently, there is a nonzero vector which is not cyclic.
We show that each power bounded operator on a Hilbert space with spectral radius equal to one has a nonzero vector which is not supercyclic. Equivalently, the operator has a nontrivial closed invariant homogeneous subset. Moreover, the operator has a nontrivial closed invariant positive cone.
6.
7.
V. M. Tyurin 《Mathematical Notes》1999,66(1):120-123
The invertibility and injectivity properties of linear differential operators with closed range and Poisson coefficients are
studied in the context of their equivalence in several spaces of vector functions defined on the axis.
Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 143–147, January, 1999. 相似文献
8.
Janusz Matkowski 《Mathematische Nachrichten》2010,283(7):1060-1064
Let I, J ? ? be intervals. The main result says that if a superposition operator H generated by a function of two variables h: I × J → ?, H (φ)(x) ? h (x, φ (x)), maps the set BV (I, J) of all bounded variation functions, φ: I → J into the Banach space BV (I, ?) and is uniformly continuous with respect to the BV ‐norm, then h (x, y) = a (x)y + b (x), x ∈ I, y ∈ J, for some a, b ∈ BV (I, ?) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
9.
Vladimir Müller 《Journal of Functional Analysis》2007,246(2):385-399
We construct a power bounded operator on a Hilbert space which is not quasisimilar to a contraction. To this aim, we solve an open problem from operator ergodic theory showing that there are power bounded Hilbert space operators without the Blum-Hanson property. We also find an example of a power bounded operator quasisimilar to a unitary operator which is not similar to a contraction, thus answering negatively open questions raised by Kérchy and Cassier. On the positive side, we prove that contractions on ?p spaces (1?p<∞) possess the Blum-Hanson property. 相似文献
10.
Ying-Fen Lin 《Journal of Mathematical Analysis and Applications》2011,382(1):469-473
In this paper, we characterize surjective completely bounded disjointness preserving linear operators on Fourier algebras of locally compact amenable groups. We show that such operators are given by weighted homomorphisms induced by piecewise affine proper maps. 相似文献
11.
Pablo Galindo Mikael Lindströ m Ray Ryan 《Proceedings of the American Mathematical Society》2000,128(1):149-155
We prove a characterization (up to the approximation property) of weakly compact composition operators in terms of their inducing analytic maps .
12.
Let U be the unilateral shift on ?2. For any complex numbers α and β, put T = αU + βU* and S = T 2. Then we show that the operator S is convexoid. 相似文献
13.
Jipu Ma 《中国科学A辑(英文版)》1997,40(12):1233-1238
A generalized dimension is further developed. Here subtraction and addition of two generalized dimensions are defined, so
that the operations: ∞ ± n = ∞, ∞ + ∞ = ∞, which used to play an inflexible role, are refined and moreover, ∞ - ∞, which used
to be meaningless, is done in sense. Then generalized index for semi-Fred-holm operators is developed to wholeB(H), i.e. all of bounded linear operators in Hilbert spaceH. Theorem 2.2 is proved with an example, which is in contradiction to a known proposition for semi-Fredholm operators in form,
practically a refined result of the known proposition. Then, it is proved thatB(H) is the union of countably many disjoint arewise connected sets over all the generalized dimensions ofB(H).
Project supported by the National Natural Science Foundation of China 相似文献
14.
Let H
1, H
2 be Hilbert spaces and T be a closed linear operator defined on a dense subspace D(T) in H
1 and taking values in H
2. In this article we prove the following results:
We prove all the above results without using the spectral theorem. Also, we give examples to illustrate all the above results. 相似文献
(i) | Range of T is closed if and only if 0 is not an accumulation point of the spectrum σ(T*T) of T*T, In addition, if H 1 = H 2 and T is self-adjoint, then |
(ii) | inf {‖T x‖: x ∈ D(T) ∩ N(T)⊥‖x‖ = 1} = inf {|λ|: 0 ≠ λ ∈ σ(T)} |
(iii) | Every isolated spectral value of T is an eigenvalue of T |
(iv) | Range of T is closed if and only if 0 is not an accumulation point of the spectrum σ(T) of T |
(v) | σ(T) bounded implies T is bounded. |
15.
Sarah H. Ferguson 《Proceedings of the American Mathematical Society》1996,124(9):2779-2785
In this paper, we consider the Ext functor in the category
of Hilbert modules over the disk algebra. We characterize the group
as a quotient of operators and explicitly calculate
, where is a weighted Hardy space. We then use our results to give a simple proof of a result due to Bourgain.
of Hilbert modules over the disk algebra. We characterize the group
as a quotient of operators and explicitly calculate
, where is a weighted Hardy space. We then use our results to give a simple proof of a result due to Bourgain.
16.
17.
A Riesz-type representation theorem is given for all positive linear endomorphisms of the space of continuous functions on a compact interval. 相似文献
18.
19.
P. Galindo M. L. Lourenç o L. A. Moraes 《Proceedings of the American Mathematical Society》2004,132(10):2917-2927
We study the class of Banach algebra-valued -homogeneous polynomials generated by the powers of linear operators. We compare it with the finite type polynomials. We introduce a topology on similar to the weak topology, to clarify the features of these polynomials.