共查询到20条相似文献,搜索用时 31 毫秒
1.
G. Corach 《Linear algebra and its applications》2011,434(6):1594-1609
We characterize the sets X of all products PQ, and Y of all products PQP, where P,Q run over all orthogonal projections and we solve the problems argmin{‖P-Q‖:(P,Q)∈Z}, for Z=X or Y. We also determine the polar decompositions and Moore-Penrose pseudoinverses of elements of X. 相似文献
2.
Claus Michael Ringel 《Journal of Pure and Applied Algebra》2006,205(2):412-422
Let Λ be a commutative local uniserial ring with radical factor field k. We consider the category S(Λ) of embeddings of all possible submodules of finitely generated Λ-modules. In case Λ=Z/〈pn〉, where p is a prime, the problem of classifying the objects in S(Λ), up to isomorphism, has been posed by Garrett Birkhoff in 1934. In this paper we assume that Λ has Loewy length at least seven. We show that S(Λ) is controlled k-wild with a single control object I∈S(Λ). It follows that each finite dimensional k-algebra can be realized as a quotient End(X)/End(X)I of the endomorphism ring of some object X∈S(Λ) modulo the ideal End(X)I of all maps which factor through a finite direct sum of copies of I. 相似文献
3.
S.W. Drury 《Linear algebra and its applications》2011,435(2):323-329
We present an effective algorithm for estimating the norm of an operator mapping a low-dimensional ?p space to a Banach space with an easily computable norm. We use that algorithm to show that Matsaev’s proposed extension of the inequality of John von Neumann is false in case p=4. Matsaev conjectured that for every contraction T on Lp (1<p<∞) one has for any polynomial P
‖P(T)‖Lp→Lp?‖P(S)‖?p(Z+)→?p(Z+) 相似文献
4.
Malliavin's celebrated theorem on the failure of spectral synthesis for the Fourier algebra A(G) on nondiscrete abelian groups was strengthened to give failure of weak synthesis by Parthasarathy and Varma. We extend this to nonabelian groups by proving that weak synthesis holds for A(G) if and only if G is discrete. We give the injection theorem and the inverse projection theorem for weak X-spectral synthesis, as well as a condition for the union of two weak X-spectral sets to be weak X-spectral for an A(G)-submodule X of VN(G). Relations between weak X-synthesis in A(G) and A(G×G) and the Varopoulos algebra V(G) are explored. The concept of operator synthesis was introduced by Arveson. We extend several recent investigations on operator synthesis by defining and studying, for a V∞(G)-submodule M of B(L2(G)), sets of weak M-operator synthesis. Relations between X-Ditkin sets and M-operator Ditkin sets and between weak X-spectral synthesis and weak M-operator synthesis are explored. 相似文献
5.
Xiaofei Qi 《Linear algebra and its applications》2010,432(12):3183-1146
Let N be a nest on a complex Banach space X with N∈N complemented in X whenever N-=N, and let AlgN be the associated nest algebra. We say that an operator Z∈AlgN is an all-derivable point of AlgN if every linear map δ from AlgN into itself derivable at Z (i.e. δ(A)B+Aδ(B)=δ(Z) for any A,B∈A with AB=Z) is a derivation. In this paper, it is shown that if Z∈AlgN is an injective operator or an operator with dense range, or an idempotent operator with ran(Z)∈N, then Z is an all-derivable point of AlgN. Particularly, if N is a nest on a complex Hilbert space, then every idempotent operator with range in N, every injective operator as well as every operator with dense range in AlgN is an all-derivable point of the nest algebra AlgN. 相似文献
6.
A. Chigogidze 《Topology and its Applications》2010,157(4):774-863
We give a short answer to the question in the title: dendrits. Precisely we show that the C*-algebra C(X) of all complex-valued continuous functions on a compactum X is projective in the category C1 of all (not necessarily commutative) unital C*-algebras if and only if X is an absolute retract of dimension dimX?1 or, equivalently, that X is a dendrit. 相似文献
7.
Roberto Muñoz 《manuscripta mathematica》1997,94(1):427-435
In this note we classify the complex projectiven-foldsX ? ? N with dimension equal to the dimension of its dualX* minus one,n ≤ 2/3N and positive defect. We show that suchn-folds are hyperplane sections of then + 1-folds withdim X=dim X* (classified by Ein) and some scrolls over curves. The natural generalization is to consider the setS p of positive defectn-folds withdim(X)=dim(X*) ? (p ? 1) (p a fixed positive integer). We show that the set of possible values of the pair (N,n) withn ≤ 2/3N corresponding to nondegeneraten-folds inS p which are not scrolls is finite. 相似文献
8.
William T. Trotter 《Discrete Mathematics》1975,12(2):165-172
In this paper we define the n-cube Qn as the poset obtained by taking the cartesian product of n chains each consisting of two points. For a finite poset X, we then define dim2X as the smallest positive integer n such that X can be embedded as a subposet of Qn. For any poset X we then have log2 |X| ? dim2X ? |X|. For the distributive lattice , dim2L = |X| and for the crown Skn, dim2 (Skn) = n + k. For each k ? 2, there exist positive constants c1 and c2 so that for the poset X consisting of all one element and k-element subsets of an n-element set, the inequality c1 log2n < dim2(X) < c2 log2n holds for all n with k < n. A poset is called Q-critical if dim2 (X ? x) < dim2(X) for every x ? X. We define a join operation ⊕ on posets under which the collection Q of all Q-critical posets which are not chains forms a semigroup in which unique factorization holds. We then completely determine the subcollection ? Q consisting of all posets X for which dim2 (X) = |X|. 相似文献
9.
Let L(X) be the algebra of all bounded linear operators on an infinite dimensional complex Banach space X. We characterize additive continuous maps from L(X) onto itself which compress the local spectrum and the convexified local spectrum at a nonzero fixed vector. Additive continuous maps from L(X) onto itself that preserve the local spectral radius at a nonzero fixed vector are also characterized. 相似文献
10.
Let B(X) be the algebra of all bounded linear operators on a complex Banach space X. We give the concrete form of every unital surjective map φ on B(X) such that AB is a non-zero idempotent if and only if φ(A)φ(B) is for all A,B∈B(X) when the dimension of X is at least 3. 相似文献
11.
《Topology and its Applications》1988,29(2):185-205
We show that strong homology groups H̄p(X; G) of a space X vanish if p is greater than the shape dimension sd X. For p=sd X, H̄p(X; G) coincides with the Čech homology groups Ȟp(X; G). We also show that there exist 1-dimensional spaces, which do not admit 1-dimensional ANR-resolutions. Therefore, the vanishing of H̄p(X; G) for p>dim X is a nontrivial fact. 相似文献
12.
Christian Le Merdy 《Advances in Mathematics》2010,224(4):1641-2998
Let G be an amenable group, let X be a Banach space and let π:G→B(X) be a bounded representation. We show that if the set is γ-bounded then π extends to a bounded homomorphism w:C∗(G)→B(X) on the group C∗-algebra of G. Moreover w is necessarily γ-bounded. This extends to the Banach space setting a theorem of Day and Dixmier saying that any bounded representation of an amenable group on Hilbert space is unitarizable. We obtain additional results and complements when G=Z, R or T, and/or when X has property (α). 相似文献
13.
Arnold W. Miller 《Topology and its Applications》2009,156(5):872-878
For X a separable metric space define p(X) to be the smallest cardinality of a subset Z of X which is not a relative γ-set in X, i.e., there exists an ω-cover of X with no γ-subcover of Z. We give a characterization of p(ω2) and p(ωω) in terms of definable free filters on ω which is related to the pseudo-intersection number p. We show that for every uncountable standard analytic space X that either p(X)=p(ω2) or p(X)=p(ωω). We show that the following statements are each relatively consistent with ZFC: (a) p=p(ωω)<p(ω2) and (b) p<p(ωω)=p(ω2) 相似文献
14.
Ronglu Li 《Topology and its Applications》2007,154(6):1195-1205
For classical Banach sequence spaces c0(X), l∞(X) and lp(X) (0<p<+∞) we have found the strongest intrinsical meanings of their β-duals, and two basic convergence results are established in the β-duals. 相似文献
15.
B.P. Duggal 《Linear algebra and its applications》2008,428(4):1109-1116
A Hilbert space operator A∈B(H) is p-hyponormal, A∈(p-H), if |A∗|2p?|A|2p; an invertible operator A∈B(H) is log-hyponormal, A∈(?-H), if log(TT∗)?log(T∗T). Let dAB=δAB or ?AB, where δAB∈B(B(H)) is the generalised derivation δAB(X)=AX-XB and ?AB∈B(B(H)) is the elementary operator ?AB(X)=AXB-X. It is proved that if A,B∗∈(?-H)∪(p-H), then, for all complex λ, , the ascent of (dAB-λ)?1, and dAB satisfies the range-kernel orthogonality inequality ‖X‖?‖X-(dAB-λ)Y‖ for all X∈(dAB-λ)-1(0) and Y∈B(H). Furthermore, isolated points of σ(dAB) are simple poles of the resolvent of dAB. A version of the elementary operator E(X)=A1XA2-B1XB2 and perturbations of dAB by quasi-nilpotent operators are considered, and Weyl’s theorem is proved for dAB. 相似文献
16.
Jean-Christophe Bourin 《Linear algebra and its applications》2006,413(1):212-217
We review some recent convexity results for Hermitian matrices and we add a new one to the list: Let A be semidefinite positive, let Z be expansive, Z∗Z?I, and let f:[0,∞)→[0,∞) be a concave function. Then, for all symmetric norms
‖f(Z∗AZ)‖?‖Z∗f(A)Z‖. 相似文献
17.
Dmitri Shakhmatov 《Topology and its Applications》2010,157(8):1518-324
Let G be a topological group with the identity element e. Given a space X, we denote by Cp(X,G) the group of all continuous functions from X to G endowed with the topology of pointwise convergence, and we say that X is: (a) G-regular if, for each closed set F⊆X and every point x∈X?F, there exist f∈Cp(X,G) and g∈G?{e} such that f(x)=g and f(F)⊆{e}; (b) G?-regular provided that there exists g∈G?{e} such that, for each closed set F⊆X and every point x∈X?F, one can find f∈Cp(X,G) with f(x)=g and f(F)⊆{e}. Spaces X and Y are G-equivalent provided that the topological groups Cp(X,G) and Cp(Y,G) are topologically isomorphic.We investigate which topological properties are preserved by G-equivalence, with a special emphasis being placed on characterizing topological properties of X in terms of those of Cp(X,G). Since R-equivalence coincides with l-equivalence, this line of research “includes” major topics of the classical Cp-theory of Arhangel'ski? as a particular case (when G=R).We introduce a new class of TAP groups that contains all groups having no small subgroups (NSS groups). We prove that: (i) for a given NSS group G, a G-regular space X is pseudocompact if and only if Cp(X,G) is TAP, and (ii) for a metrizable NSS group G, a G?-regular space X is compact if and only if Cp(X,G) is a TAP group of countable tightness. In particular, a Tychonoff space X is pseudocompact (compact) if and only if Cp(X,R) is a TAP group (of countable tightness). Demonstrating the limits of the result in (i), we give an example of a precompact TAP group G and a G-regular countably compact space X such that Cp(X,G) is not TAP.We show that Tychonoff spaces X and Y are T-equivalent if and only if their free precompact Abelian groups are topologically isomorphic, where T stays for the quotient group R/Z. As a corollary, we obtain that T-equivalence implies G-equivalence for every Abelian precompact group G. We establish that T-equivalence preserves the following topological properties: compactness, pseudocompactness, σ-compactness, the property of being a Lindelöf Σ-space, the property of being a compact metrizable space, the (finite) number of connected components, connectedness, total disconnectedness. An example of R-equivalent (that is, l-equivalent) spaces that are not T-equivalent is constructed. 相似文献
18.
For K a set of topological spaces and X,Y∈K, the notation Xh⊆Y means that X embeds homeomorphically into Y; and X∼Y means Xh⊆Yh⊆X. With , the equivalence relation ∼ on K induces a partial order h? well-defined on K/∼ as follows: if Xh⊆Y.For posets (P,P?) and (Q,Q?), the notation (P,P?)?(Q,Q?) means: there is an injection such that p0P?p1 in P if and only if h(p0)Q?h(p1) in Q. For κ an infinite cardinal, a poset (Q,Q?) is a κ-universal poset if every poset (P,P?) with |P|?κ satisfies (P,P?)?(Q,Q?).The authors prove two theorems which improve and extend results from the extensive relevant literature.
Theorem 2.2.
There is a zero-dimensional Hausdorff space S with|S|=κsuch that(P(S)/∼,h?)is a κ-universal poset. 相似文献
19.
Abdellatif Bourhim 《Linear algebra and its applications》2010,432(1):383-1478
Let B(X) be the algebra of all bounded linear operators on an infinite dimensional complex Banach space X. We characterize linear surjective and continuous maps on B(X) preserving different local spectral quantities at a nonzero fixed vector. 相似文献
20.
Two perturbation estimates for maximal positive definite solutions of equations X + A*X−1A = Q and X − A*X−1A = Q are considered. These estimates are proved in [Hasanov et al., Improved perturbation Estimates for the Matrix Equations X ± A*X−1A = Q, Linear Algebra Appl. 379 (2004) 113-135]. We derive new perturbation estimates under weaker restrictions on coefficient matrices of the equations. The theoretical results are illustrated by numerical examples. 相似文献