共查询到20条相似文献,搜索用时 62 毫秒
1.
Wiesław Śliwa 《Czechoslovak Mathematical Journal》2004,54(2):457-463
We prove that any infinite-dimensional non-archimedean Fréchet space E is homeomorphic to
where D is a discrete space with card(D) = dens(E). It follows that infinite-dimensional non-archimedean Fréchet spaces E and F are homeomorphic if and only if dens(E) = dens(F). In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field
is homeomorphic to the non-archimedean Fréchet space
. 相似文献
2.
The aim of this note is to investigate the topological structure (in particular the density condition) of subspaces and separated quotients of Fréchet spaces. Our main result is the following one: LetE be a Fréchet space which is neither Montel nor isomorphic to a closed subspace ofX × , withX a Banach space, also assume thatE can be written asFG withF andG infinite dimensional closed subspaces ofE not isomorphic to , thenE contains a closed subspace with basis and not satisfying the density condition. We also prove that every Köthe echelon space of orderp, 1<p<, which is not quasinormable has a separated quotient with basis which does not satisfy the density condition. 相似文献
3.
Martin Blümlinger 《manuscripta mathematica》1989,65(3):377-384
The maximal ideal space of the Fréchet spaceBV
is determined and topological properties are given. It is shown that the Banach algebraBV has properties D and N*, but does not have property N for dimensions higher than 1. 相似文献
4.
Christopher Boyd 《Czechoslovak Mathematical Journal》2003,53(2):365-376
For U a balanced open subset of a Fréchet space E and F a dual-Banach space we introduce the topology on the space
of holomorphic functions from U into F. This topology allows us to construct a predual for
which in turn allows us to investigate the topological structure of spaces of vector-valued holomorphic functions. In particular, we are able to give necessary and sufficient conditions for the equivalence and compatibility of various topologies on spaces of vector-valued holomorphic functions. 相似文献
5.
We study the Hermite transform onL
2() where is a Gaussian measure on a Lusin locally convex spaceE. We are then lead to a Hilbert space () of analytic functions onE which is also a natural range for the Laplace transform. LetB be a convenient Hilbert-Schmidt operator on the Cameron-Martin spaceH of . There exists a natural sequence Cap
n
of capacities onE associated toB. This implies the Kondratev-Yokoi theorem about positive linear forms on the Hida test-functions space. 相似文献
6.
The following results are presented: 1) a characterization through the Liouville property of those Stein manifoldsU such that every germ of holomorphic functions on xU can be developed locally as a vector-valued Taylor series in the first variable with values inH(U); 2) ifT
is a surjective convolution operator on the space of scalar-valued real analytic functions, one can find a solutionu of the equationT
u=f which depends holomorphically on the parameterz wheneverf depends in the same manner. These results are obtained as an application of a thorough study of vector-valued real analytic maps by means of the modern functional analytic tools. In particular, we give a tensor product representation and a characterization of those Fréchet spaces or LB-spacesE for whichE-valued real analytic functions defined via composition with functionals and via suitably convergent Taylor series are the same. 相似文献
7.
N. L. Vasilevski 《Integral Equations and Operator Theory》1998,31(1):113-132
We study the following problem: Given a Hilbert spaceH and a set of orthogonal projectionsP, Q
1, ..., Qn on it, with the conditionsQ
j
·Q
k
=
j,k
Q
k
,
, describe theC
*-algebraC
*(P, Q
1, ..., Qn) generated by these projections.Applications to Naimark dilation theorems and to Toeplitz operators associated with the Heisenberg group are given.Dedicated to the memory of M. G. Krein.This work was partially supported by CONACYT Project 3114P-E9608, México. 相似文献
8.
LetM be a von Neumann algebra with a faithful normal tracial state and letH
be a finite maximal subdiagonal subalgebra ofM. LetH
2 be the closure ofH
in the noncommutative Lebesgue spaceL
2(M). We consider Toeplitz operators onH
2 whose symbol belong toM, and find that they possess several of the properties of Toeplitz operators onH
2(
) with symbol fromL
(
), including norm estimates, a Hartman-Wintner spectral inclusion theorem, and a characterisation of the weak* continuous linear functionals on the space of Toeplitz operators. 相似文献
9.
Fréchet-Urysohn (briefly F-U) property for topological spaces is known to be highly non-multiplicative; for instance, the square of a compact F-U space is not in general Fréchet-Urysohn [P. Simon, A compact Fréchet space whose square is not Fréchet, Comment. Math. Univ. Carolin. 21 (1980) 749-753. [27]]. Van Douwen proved that the product of a metrizable space by a Fréchet-Urysohn space may not be (even) sequential. If the second factor is a topological group this behaviour improves significantly: we have obtained (Theorem 1.6(c)) that the product of a first countable space by a F-U topological group is a F-U space. We draw some important consequences by interacting this fact with Pontryagin duality theory. The main results are the following:
- (1)
- If the dual group of a metrizable Abelian group is F-U, then it must be metrizable and locally compact.
- (2)
- Leaning on (1) we point out a big class of hemicompact sequential non-Fréchet-Urysohn groups, namely: the dual groups of metrizable separable locally quasi-convex non-locally precompact groups. The members of this class are furthermore complete, strictly angelic and locally quasi-convex.
- (3)
- Similar results are also obtained in the framework of locally convex spaces.
10.
M. Fragoulopoulou 《Periodica Mathematica Hungarica》1988,19(3):181-208
V. Pták's inequality is valid for every hermitian completeQ locallym-convex (:l.m.c.) algebra. Every algebra of the last kind is, in particular, symmetric. Besides, a (Hausdorff) locallyC
*-algebra (being always symmetric) with the propertyQ is, within a topological algebraic isomorphism, aC
*-algebra. Furthermore, a type of Raikov's criterion for symmetry is also valid for non-normed topological*-algebras. Concerning topological tensor products, one gets that symmetry of the-completed tensor product of two unital Fréchet l.m.c.*-algebrasE, F ( denotes the projective tensorial topology) is always passed toE, F, while the converse occurs when moreover either ofE, F is commutative. 相似文献
11.
For a given linear topology , on a vector spaceE, the finest linear topology having the same convergent sequences, and the finest linear topology onE having the same precompact sets, are investigated. Also, the sequentially bornological spaces and the sequentially barreled spaces are introduced and some of their properties are studied. 相似文献
12.
We identify the universal differential module 1(A) for the Fréchet algebra A of holomorphic functions on a complex Stein manifold X, and more generally on a Riemannian domain R over X and for the algebra of germs of holomorphic functions on a compact subset K
n
. It turns out to be isomorphic to the Fréchet space of holomorphic 1-forms on X, resp. R, resp. to the space 1(K) of germs of holomorphic 1-forms in K. This determines the center of the universal central extension of the Lie algebra (R, of holomorphic maps from R to a finite-dimensional simple complex Lie algebra . 相似文献
13.
Ghislain Vaillant 《Integral Equations and Operator Theory》1995,22(3):339-351
In this note we show that a separable C*-algebra is nuclear and has a quasidiagonal extension by
(the ideal of compact operators on an infinite-dimensional separable Hilbert space) if and only if it is anuclear finite algebra (NF-algebra) in the sense of Blackadar and Kirchberg, and deduce that every nuclear C*-subalgebra of aNF-algebra isNF. We show that strongNF-algebras satisfy a Følner type condition. 相似文献
14.
Parameter dependence of solutions of differential equations on spaces of distributions and the splitting of short exact sequences 总被引:1,自引:0,他引:1
We show that a linear partial differential operator with constant coefficients P(D) is surjective on the space of E-valued (ultra-)distributions over an arbitrary convex set if E′ is a nuclear Fréchet space with property (DN). In particular, this holds if E is isomorphic to the space of tempered distributions S′ or to the space of germs of holomorphic functions over a one-point set H({0}). This result has an interpretation in terms of solving the scalar equation P(D)u=f such that the solution u depends on parameter whenever the right-hand side f also depends on the parameter in the same way. A suitable analogue for surjective convolution operators over is obtained as well. To get the above results we develop a splitting theory for short exact sequences of the form
0XYZ0,