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1.
Let B(X) be the algebra of all bounded linear operators on the Banach space X, and let N(X) be the set of nilpotent operators in B(X). Suppose ?:B(X)→B(X) is a surjective map such that A,BB(X) satisfy ABN(X) if and only if ?(A)?(B)∈N(X). If X is infinite dimensional, then there exists a map f:B(X)→C?{0} such that one of the following holds:
(a)
There is a bijective bounded linear or conjugate-linear operator S:XX such that ? has the form A?S[f(A)A]S-1.
(b)
The space X is reflexive, and there exists a bijective bounded linear or conjugate-linear operator S : X′ → X such that ? has the form A ? S[f(A)A′]S−1.
If X has dimension n with 3 ? n < ∞, and B(X) is identified with the algebra Mn of n × n complex matrices, then there exist a map f:MnC?{0}, a field automorphism ξ:CC, and an invertible S ∈ Mn such that ? has one of the following forms:
  相似文献   

2.
Suppose that is a collection of disjoint subcontinua of continuum X such that limi→∞dH(Yi,X)=0 where dH is the Hausdorff metric. Then the following are true:
(1)
X is non-Suslinean.
(2)
If each Yi is chainable and X is finitely cyclic, then X is indecomposable or the union of 2 indecomposable subcontinua.
(3)
If X is G-like, then X is indecomposable.
(4)
If all lie in the same ray and X is finitely cyclic, then X is indecomposable.
  相似文献   

3.
Let H be a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. An operator A in L(H) is said to be a Cowen-Douglas operator if there exist Ω, a connected open subset of complex plane C, and n, a positive integer, such that
(a)
(b)
  for z in Ω;
(c)
; and
(d)
for z in Ω.
In the paper, we give a similarity classification of Cowen-Douglas operators by using the ordered K-group of the commutant algebra as an invariant, and characterize the maximal ideals of the commutant algebras of Cowen-Douglas operators. The theorem greatly generalizes the main result in (Canada J. Math. 156(4) (2004) 742) by simply removing the restriction of strong irreducibility of the operators. The research is also partially inspired by the recent classification theory of simple AH algebras of Elliott-Gong in (Documenta Math. 7 (2002) 255; On the classification of simple inductive limit C*-algebras, II: The isomorphism theorem, preprint.) (also see (J. Funct. Anal. (1998) 1; Ann. Math. 144 (1996) 497; Amer. J. Math. (1996) 187)).  相似文献   

4.
Let M be the Cantor space or an n-dimensional manifold with C(M,M) the set of continuous self-maps of M, and . We prove the following:
(1)
If α≠∞, then Sα(M) is a nowhere dense subset of M×C(M,M) that contains no isolated points.
(2)
If α?β, then .
  相似文献   

5.
We prove the following: Let A and B be separable C*-algebras. Suppose that B is a type I C*-algebra such that
(i)
B has only infinite dimensional irreducible *-representations, and
(ii)
B has finite decomposition rank.
If
0→BCA→0  相似文献   

6.
We continue the study of the Hochschild structure of a smooth space that we began in our previous paper, examining implications of the Hochschild-Kostant-Rosenberg theorem. The main contributions of the present paper are:
we introduce a generalization of the usual notions of Mukai vector and Mukai pairing on differential forms that applies to arbitrary manifolds;
we give a proof of the fact that the natural Chern character map K0(X)→HH0(X) becomes, after the HKR isomorphism, the usual one ; and
we present a conjecture that relates the Hochschild and harmonic structures of a smooth space, similar in spirit to the Tsygan formality conjecture.
  相似文献   

7.
It is proved in this paper that for a continuous B-domain L, the function space [XL] is continuous for each core compact and coherent space X. Further, applications are given. It is proved that:
(1)
the function space from the unit interval to any bifinite domain which is not an L-domain is not Lawson compact;
(2)
the Isbell and Scott topologies on [XL] agree for each continuous B-domain L and core compact coherent space X.
  相似文献   

8.
For a space X, X2 denotes the collection of all non-empty closed sets of X with the Vietoris topology, and K(X) denotes the collection of all non-empty compact sets of X with the subspace topology of X2. The following are known:
ω2 is not normal, where ω denotes the discrete space of countably infinite cardinality.
For every non-zero ordinal γ with the usual order topology, K(γ) is normal iff whenever cf γ is uncountable.
In this paper, we will prove:
(1)
ω2 is strongly zero-dimensional.
(2)
K(γ) is strongly zero-dimensional, for every non-zero ordinal γ.
In (2), we use the technique of elementary submodels.  相似文献   

9.
10.
We introduce representable Banach spaces, and prove that the class R of such spaces satisfies the following properties:
(1)
Every member of R has the Daugavet property.
(2)
It Y is a member of R, then, for every Banach space X, both the space L(X,Y) (of all bounded linear operators from X to Y) and the complete injective tensor product lie in R.
(3)
If K is a perfect compact Hausdorff topological space, then, for every Banach space Y, and for most vector space topologies τ on Y, the space C(K,(Y,τ)) (of all Y-valued τ-continuous functions on K) is a member of R.
(4)
If K is a perfect compact Hausdorff topological space, then, for every Banach space Y, most C(K,Y)-superspaces (in the sense of [V. Kadets, N. Kalton, D. Werner, Remarks on rich subspaces of Banach spaces, Studia Math. 159 (2003) 195-206]) are members of R.
(5)
All dual Banach spaces without minimal M-summands are members of R.
  相似文献   

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