共查询到20条相似文献,搜索用时 36 毫秒
1.
Jintana Sanwong 《Semigroup Forum》2011,83(1):134-146
Let T(X) be the full transformation semigroup on the set X and let T(X,Y) be the semigroup consisting of all total transformations from X into a fixed subset Y of X. It is known that $$F(X, Y)=\{\alpha\in T(X, Y): X\alpha\subseteq Y\alpha\},$$ is the largest regular subsemigroup of T(X,Y) and determines Green??s relations on T(X,Y). In this paper, we show that F(X,Y)?T(Z) if and only if X=Y and |Y|=|Z|; or |Y|=1=|Z|, and prove that every regular semigroup S can be embedded in F(S 1,S). Then we describe Green??s relations and ideals of F(X,Y) and apply these results to get all of its maximal regular subsemigroups when Y is a nonempty finite subset of X. 相似文献
2.
Let T(X) be the full transformation semigroup on the set X and let T(X,Y) be the semigroup consisting of all total transformations from X into a fixed nonempty subset Y of X. In 2011, Sanwong studied the regular part $$F(X,Y)=\bigl\{\alpha\in T(X,Y): X\alpha\subseteq Y\alpha\bigr\}, $$ of T(X,Y) and described its Green’s relations and ideals. In this paper, we compute the rank of F(X,Y) when X is a finite set. Moreover, we obtain the rank and idempotent rank of its ideals. 相似文献
3.
Lei Sun 《Semigroup Forum》2013,87(3):681-684
Given a set X and a nonempty Y?X, we denote by T(X,Y) the subsemigroup of the full transformation semigroup on X consisting of all transformations whose range is contained in Y. We show that the semigroup T(X,Y) is right abundant but not left abundant whenever Y is a proper non-singleton subset of X. 相似文献
4.
Denote by T(X) the semigroup of full transformations on a set X. For ε∈T(X), the centralizer of ε is a subsemigroup of T(X) defined by C(ε)={α∈T(X):αε=εα}. It is well known that C(id
X
)=T(X) is a regular semigroup. By a theorem proved by J.M. Howie in 1966, we know that if X is finite, then the subsemigroup generated by the idempotents of C(id
X
) contains all non-invertible transformations in C(id
X
). 相似文献
5.
R. W. Cross 《Mathematische Nachrichten》1996,178(1):103-116
Let L(X,Y) denote the class of linear transformations T:D(T) ? X → Y where X and Y are normed spaces. A quantity f is called densely invariant if for every system L(X, Y) and every operator T ? L(X,Y) we have f(T/E)= f(T) whenever E is a core of T. The density invariance of certain well known quantities is established. In case Y is complete and T is closable, a stronger property is shown to hold for some of these quantitites, namely invariance under restriction to dense subspaces. 相似文献
6.
Theω′-topology on the spaceL(X, Y) of bounded linear operators from the Banach spaceX into the Banach spaceY is discussed in [10]. Let ℒw' (X, Y) denote the space of allT∈L(X, Y) for which there exists a sequence of compact linear operators (T
n)⊂K(X, Y) such thatT=ω′−limnTn and let
. We show that
is a Banach ideal of operators and that the continuous dual spaceK(X, Y)* is complemented in
. This results in necessary and sufficient conditions forK(X, Y) to be reflexive, whereby the spacesX andY need not satisfy the approximation property. Similar results follow whenX andY are locally convex spaces.
Financial support from the Potchefstroom University and Maseno University is greatly acknowledged.
Financial support from the NRF and Potchefstroom University is greatly acknowledged. 相似文献
7.
Let [A, a] be a normed operator ideal. We say that [A, a] is boundedly weak*-closed if the following property holds: for all Banach spaces X and Y, if T: X → Y** is an operator such that there exists a bounded net (T
i
)
i∈I
in A(X, Y) satisfying lim
i
〈y*, T
i
x
y*〉 for every x ∈ X and y* ∈ Y*, then T belongs to A(X, Y**). Our main result proves that, when [A, a] is a normed operator ideal with that property, A(X, Y) is complemented in its bidual if and only if there exists a continuous projection from Y** onto Y, regardless of the Banach space X. We also have proved that maximal normed operator ideals are boundedly weak*-closed but, in general, both concepts are different.
相似文献
8.
HaoBoYANG XiuLiangYANG 《数学学报(英文版)》2004,20(3):475-482
Let Tn be the full transformation semigroup on the n-element set Xn. For an arbitrary integer r such that 2 ≤ r ≤ n-1, we completely describe the maximal subsemigroups of the semigroup K(n, r) = {α∈Tn : |im α| ≤ r}. We also formulate the cardinal number of such subsemigroups which is an answer to Problem 46 of Tetrad in 1969, concerning the number of subsemigroups of Tn. 相似文献
9.
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
10.
MiaoLI QuanZHENG 《数学学报(英文版)》2004,20(5):821-828
Let T = (T(t))t≥0 be a bounded C-regularized semigroup generated by A on a Banach space X and R(C) be dense in X. We show that if there is a dense subspace Y of X such that for every x ∈ Y, σu(A, Cx), the set of all points λ ∈ iR to which (λ - A)^-1 Cx can not be extended holomorphically, is at most countable and σr(A) N iR = Ф, then T is stable. A stability result for the case of R(C) being non-dense is also given. Our results generalize the work on the stability of strongly continuous senfigroups. 相似文献
11.
Let X and Y be Banach spaces. A set
(the space of all weakly compact operators from X into Y) is weakly equicompact if, for every bounded sequence (x
n) in X, there exists a subsequence (x
k(n)) so that (Txk(n)) is uniformly weakly convergent for T ∈ M. In this paper, the notion of weakly equicompact set is used to obtain characterizations of spaces X such that
X ↩̸ ℓ1, of spaces X such that B
X*
is weak* sequentially compact and also to obtain several results concerning to the weak operator and the strong operator
topologies. As another application of weak equicompactness, we conclude a characterization of relatively compact sets in
when this space is endowed with the topology of uniform convergence on the class of all weakly null sequences. Finally, we
show that similar arguments can be applied to the study of uniformly completely continuous sets.
Received: 5 July 2006 相似文献
12.
T. S. S. R. K. Rao 《Proceedings Mathematical Sciences》1999,109(1):75-85
For 1 ≤p ≤ ∞ we show that there are no denting points in the unit ball of ℓ(lp). This extends a result recently proved by Grząślewicz and Scherwentke whenp = 2 [GS1]. We also show that for any Banach spaceX and for any measure space (Ω, A, μ), the unit ball of ℓ(L
1 (μ), X) has denting points iffL
1(μ) is finite dimensional and the unit ball ofX has a denting point. We also exhibit other classes of Banach spacesX andY for which the unit ball of ℓ(X, Y) has no denting points. When X* has the extreme point intersection property, we show that all ‘nice’ operators in the unit
ball of ℓ(X, Y) are strongly extreme points. 相似文献
13.
LetT(t) be the translation group onY=C
0(ℝ×K)=C
0(ℝ)⊗C(K),K compact Hausdorff, defined byT(t)f(x, y)=f(x+t, y). In this paper we give several representations of the sun-dialY
⊙ corresponding to this group. Motivated by the solution of this problem, viz.Y
⊙=L
1(ℝ)⊗M(K), we develop a duality theorem for semigroups of the formT
0(t)⊗id on tensor productsZ⊗X of Banach spaces, whereT
0(t) is a semigroup onZ. Under appropriate compactness assumptions, depending on the kind of tensor product taken, we show that the sun-dial ofZ⊗X is given byZ
⊙⊗X*. These results are applied to determine the sun-dials for semigroups induced on spaces of vector-valued functions, e.g.C
0(Ω;X) andL
p
(μ;X).
This paper was written during a half-year stay at the Centre for Mathematics and Computer Science CWI in Amsterdam. I am grateful
to the CWI and the Dutch National Science Foundation NWO for financial support. 相似文献
14.
M. Rudelson 《Israel Journal of Mathematics》1995,89(1-3):189-204
We prove a variant of a theorem of N. Alon and V. D. Milman. Using it we construct for everyn-dimensional Banach spacesX andY a measure space Ω and two operator-valued functionsT: Ω→L(X, Y),S: Ω→L(Y, X) so that ∫Ω
S(ω)oT(ω)dω is the identity operator inX and ∫Ω||S(ω)||·||T(ω)||dω=O(n
α
) for some absolute constantα<1.
We prove also that any subset of the unitn-cube which is convex, symmetric with respect to the origin and has a sufficiently large volume possesses a section of big
dimension isomorphic to ak-cube.
Research supported in part by a grant of the Israel Academy of Sciences. 相似文献
15.
Let X and Y be Banach spaces. We say that a set
(the space of all weakly compact operators from X into Y) is weakly equicompact if, for every bounded sequence (xn) in X, there exists a subsequence (xk(n)) so that (Txk(n)) is weakly uniformly convergent for T ∈ M. We study some properties of weakly equicompact sets and, among other results, we prove: 1) if
is collectively weakly compact, then M* is weakly equicompact iff M** x**={T** x** : T ∈ M} is relatively compact in Y for every x** ∈X**; 2) weakly equicompact sets are precompact in
for the topology of uniform convergence on the weakly null sequences in X.
Received: 14 February 2005; revised: 1 June 2005 相似文献
16.
Regular congruences on an E-inversive semigroup 总被引:1,自引:0,他引:1
17.
Takao Yamazaki 《K-Theory》2004,31(4):289-306
Let X be a surface over a p-adic field with good reduction and let Y be its special fiber. We write T(X) and T(Y) for the kernels of the Albanese maps of X and Y, respectively. Then, F(X) = T(X)/T(X)div is conjectured to be finite, where T(X)div is the maximal divisible subgroup of T(X). Furthermore, F(X) is conjectured to be isomorphic to T(Y) modulo p-primary torsion. We show that the p-primary torsion subgroup of F(X) can be arbitrary large even though we fix the special fiber Y. 相似文献
18.
M. Valdivia 《Israel Journal of Mathematics》1990,71(3):289-296
LetY andZ be two closed subspaces of a Banach spaceX such thatY≠lcub;0rcub; andY+Z=X. Then, ifZ is weakly countably determined, there exists a continuous projectionT inX such that ∥T∥=1,T(X)⊃Y, T
−1(0)⊂Z and densT(X)=densY. It follows that every Banach spaceX is the topological direct sum of two subspacesX
1 andX
2 such thatX
1 is reflexive and densX
2**=densX**/X. 相似文献
19.
For natural numbers r,s,q,m,n with s≥r≤q we determine all natural functions g: T
*(J
(r,s,q)(Y, R
1,1)0)*→R for any fibered manifold Y with m-dimensional base and n-dimensional fibers. For natural numbers r,s,m,n with s≥r we determine all natural functions g: T
*(J
(r,s)
(Y, R)0)*→R for any Y as above. 相似文献
20.
C. Alegre 《Acta Mathematica Hungarica》2009,122(4):357-372
If (X, p) and (Y, q) are two asymmetric normed spaces, the set LC(X, Y) of all continuous linear mappings from (X, p) to (Y, q) is not necessarily a linear space, it is a cone. If X and Y are two Banach lattices and p and q are, respectively, their associated asymmetric norms (p(x) = ‖+‖, q(y) = ‖y
+‖), we prove that the positive operators from X to Y are elements of the cone LC(X, Y). We also study the dual space of an asymmetric normed space and finally we give open mapping and closed graph type theorems
in the framework of asymmetric normed spaces. The classical results for normed spaces follow as particular cases.
The author acknowledges the support of the Ministerio de Educación y Ciencia of Spain and FEDER, under grant MTM2006-14925-C02-01
and Generalitat Valenciana under grant GV/2007/198. 相似文献