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101.
P. Kasprzak 《Journal of Functional Analysis》2011,260(1):146-163
Let G1⊂G be a closed subgroup of a locally compact group G and let X=G/G1 be the quotient space of left cosets. Let X=(C0(X),ΔX) be the corresponding G-C∗-algebra where G=(C0(G),Δ). Suppose that Γ is a closed abelian subgroup of G1 and let Ψ be a 2-cocycle on the dual group . Let GΨ be the Rieffel deformation of G. Using the results of the previous paper of the author we may construct GΨ-C∗-algebra XΨ - the Rieffel deformation of X. On the other hand we may perform the Rieffel deformation of the subgroup G1 obtaining the closed quantum subgroup , which in turn, by the results of S. Vaes, leads to the GΨ-C∗-algebra . In this paper we show that . We also consider the case where Γ⊂G is not a subgroup of G1, for which we cannot construct the subgroup . Then generically XΨ cannot be identified with a quantum quotient. What may be shown is that it is a GΨ-simple object in the category of GΨ-C∗-algebras. 相似文献
102.
C.J. Read 《Journal of Mathematical Analysis and Applications》2011,381(1):202-217
We show that in every nonzero operator algebra with a contractive approximate identity (or c.a.i.), there is a nonzero operator T such that ‖I−T‖?1. In fact, there is a c.a.i. consisting of operators T with ‖I−2T‖?1. So, the numerical range of the elements of our contractive approximate identity is contained in the closed disk center and radius . This is the necessarily weakened form of the result for C?-algebras, where there is always a contractive approximate identity consisting of operators with 0?T?1 - the numerical range is contained in the real interval [0,1]. So, if an operator algebra has a c.a.i., it must have operators with a “certain amount” of positivity. 相似文献
103.
Applications of operator identities to the multiple q-binomial theorem and q-Gauss summation theorem
In this paper, we first give an interesting operator identity. Furthermore, using the q-exponential operator technique to the multiple q-binomial theorem and q-Gauss summation theorem, we obtain some transformation formulae and summation theorems of multiple basic hypergeometric series. 相似文献
104.
We construct a counterexample to Solel's [B. Solel, Contractive projections onto bimodules of von Neumann algebras, J. London Math. Soc. 45 (2) (1992) 169–179] conjecture that the range of any contractive, idempotent, MASA bimodule map on is necessarily a ternary subalgebra. Our construction reduces this problem to an analogous problem about the ranges of idempotent maps that are equivariant with respect to a group action. Such maps are important to understand Hamana's theory [M. Hamana, Injective envelopes of C*-dynamical systems, Tohoku Math. J. 37 (1985) 463–487] of G-injective operator spaces and G-injective envelopes. 相似文献
105.
In this paper we introduce the notion of operator semirings of a -semiring to study -semirings. It is shown that the lattices of all left (right) ideals (two-sided ideals) of a -semiring and its right (respectively left) operator semiring are isomorphic. This has many applications to characterize various -semirings.AMS Subject Classification (2000): 16Y60, 16Y99 相似文献
106.
L. Rodrí guez-Piazza M. C. Romero-Moreno 《Transactions of the American Mathematical Society》2000,352(1):379-395
Let be a real number such that and its conjugate exponent . We prove that for an operator defined on with values in a Banach space, the image of the unit ball determines whether belongs to any operator ideal and its operator ideal norm. We also show that this result fails to be true in the remaining cases of . Finally we prove that when the result holds in finite dimension, the map which associates to the image of the unit ball the operator ideal norm is continuous with respect to the Hausdorff metric.
107.
1.引言 对线性算子的有限秩算子逼近是最经典的问题.并且它的应用极广.如数值积分公式、函数的逼近、数值原函数、方程的数值解法等.1986年,在文[1]中,首次给出了在再生核空间中函数的最佳逼近算子(恒等算子的有限秩算子逼近).之后;在文[2]中给出了数值原函数.又在文[3]、[5]、[6]等中利用有限秩算子逼近(并非是最佳逼近)给出了一些方程的数值解法.但这些讨论都是在一元函数空间上只对特殊算子进行的.1997年,虽然在文[4]中给出了完备的二元再生核空间及二元函数的最佳逼近插值算子.但是对多元… 相似文献
108.
Let(E,r)bealocallyconvexHausdorfftopologicalvectorspace.AseriesZxiinEissaidtobesubseriesr-convergent(-s.c.),ifforeachstrictlyincreasingsequence{n,}inN,theseriesZx"'isT-convergent.TheseriesZx,issaidtobeunconditionallyr-convergent(r-u.c.),ifforeachpermutationffofN,theseriesZx,<,,ls.,r-convergence.rheseriesZx,issaidtobesubseriesunconditional1yT-convergent(r-s.u.c.)ifforeachstrictlyincreasingseqtience{n,}inN,theseriesZx.,isunconditionallyr-convergent.If(E,r)isasequentiallycompletespace,thenT… 相似文献
109.
Necessary and sufficient conditions are obtained for operator partial 2 × 2 matrices to have an idempotent completion, and
all such completions are parametrically represented.
Project supported by National Natural Science Foundation of China and Provincial Natural Science Foundation of Shanxi 相似文献
110.
Nguyen BUONG 《数学年刊B辑(英文版)》1999,20(2):255-260
51.IntroductionIn[5]wepresentedamethodofregularizationforsolvingtheoperatorequationofHammerstein'stypewhereboththeoperatorsFZ'X*-XandFI:X-X*arenonlinear,hemicontinuousandmonotone;Xisareflexive,strictlyconvexBanachspacehavingtheE-property,i.e.weakconvergenceandconvergenceofnormsforanysequenceinXfOllowitstrongconvergence,andX*denotestheadjointspaceofX.Obviously,anyuniformlyconvexBanachspacehastheE-property.FromnowonwesupposethatXandX*areuniformlyconvex.Further,forthesakeofsimplicitynorms… 相似文献