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We study when a Banach space with absolute norm may have polynomial numerical indices equal to one. In the real case, we show that a Banach space X with absolute norm, which has the Radon-Nikodým property or is Asplund, satisfies n(2)(X)<1 unless it is one-dimensional. In the complex case, we show that the only Banach spaces X with absolute norm and the Radon-Nikodým property which satisfy n(2)(X)=1 are the spaces . Also, the only Asplund complex space X with absolute norm which satisfies n(2)(X)=1 is c0(Λ). 相似文献
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B. Nagy 《Periodica Mathematica Hungarica》1980,11(1):1-6
The various essential spectra of a linear operator have been surveyed byB. Gramsch andD. Lay [4]. In this paper we characterize the essential spectra and the related quantities nullity, defect, ascent and descent of bounded spectral operators. It is shown that a number of these spectra coincide in the case of a spectral or a scalar type operator. Some results known for normal operators in Hilbert space are extended to spectral operators in Banach space. 相似文献
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Héctor N. Salas 《Archiv der Mathematik》2006,86(3):241-250
We exhibit a hypercyclic operator whose square is not hypercyclic. Our operator is necessarily unbounded since a result of
S. Ansari asserts that powers of a hypercyclic bounded operator are also hypercyclic. We also exhibit an unbounded Hilbert
space operator whose non-zero vectors are hypercyclic.
Received: 19 March 2005; revised: 18 July 2005 相似文献
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B. Yousefi 《Archiv der Mathematik》2004,83(6):536-539
Let
be a Hilbert space of functions analytic on a plane domain such that for every in the functional of evaluation at is bounded. Assume further that
contains the constants and admits multiplication by the independent variable z, Mz, as a bounded operator. We give sufficient conditions for Mz to be reflexive.Received: 17 February 2004 相似文献
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Lie-Yamaguti algebras (or generalized Lie triple systems) are binary-ternary algebras intimately related to reductive homogeneous spaces. The Lie-Yamaguti algebras which are irreducible as modules over their inner derivation algebras are the algebraic counterparts of the isotropy irreducible homogeneous spaces.These systems splits into three disjoint types: adjoint type, non-simple type and generic type. The systems of the first two types were classified in a previous paper through a generalized Tits Construction of Lie algebras. In this paper, the Lie-Yamaguti algebras of generic type are classified by relating them to several other nonassociative algebraic systems: Lie and Jordan algebras and triple systems, Jordan pairs or Freudenthal triple systems. 相似文献
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The Sz.-Nagy-FoiaŞ functional model for completely non-unitary contractions is extended to completely non-coisometric sequences
of bounded operatorsT = (T1,...,T
d) (d finite or infinite) on a Hilbert space, with bounded characteristic functions. For this class of sequences, it is shown
that the characteristic function θT is a complete unitary invariant.
We obtain, as the main result, necessary and sufficient conditions for a bounded multi-analytic operator on Fock spaces to
coincide with the characteristic function associated with a completely non-coisometric sequence of bounded operators on a
Hilbert space.
Research supported in part by a COBASE grant from the National Research Council.
The first author was partially supported by a grant from Ministerul Educaţiei Şi Cercetarii.
The second author was partially supported by a National Science Foundation grant. 相似文献
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We analyze the extent to which a quantum universal enveloping algebra of a Kac–Moody algebra g is defined by multidegrees of its defining relations. To this end, we consider a class of character Hopf algebras defined by the same number of defining relations of the same degrees as the Kac–Moody algebra g. We demonstrate that if the generalized Cartan matrix A of g is connected then the algebraic structure, up to a finite number of exceptional cases, is defined by just one “continuous” parameter q related to a symmetrization of A, and one “discrete” parameter m related to the modular symmetrizations of A. The Hopf algebra structure is defined by n(n−1)/2 additional “continuous” parameters. We also consider the exceptional cases for Cartan matrices of finite or affine types in more detail, establishing the number of exceptional parameter values in terms of the Fibonacci sequence. 相似文献
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Jagjit Singh Matharu Mohammad Sal Moslehian Jaspal Singh Aujla 《Linear algebra and its applications》2011,435(2):270-276
We present a weak majorization inequality and apply it to prove eigenvalue and unitarily invariant norm extensions of a version of the Bohr’s inequality due to Vasi? and Ke?ki?. 相似文献
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Z. Abdelali 《代数通讯》2013,41(7):2437-2452
Using Bre?ar and ?emrl approach, we give a proof of the extended Jacobson density theorem for Φ-derivations. Further, some applications on Banach algebras will be given. Precisely, for d being a continuous Φ-derivation on a given Banach algebra ?, we show that: d(?) ? rad (?) ? [b,[a, d(a)]] ∈ rad (?) for all a, b ∈ ? and d leaves invariant all maximal ideals of codimension one?for every a ∈ ? there exists a positive integer n such that (d(a)) n is quasi-nilpotent ? [d, Φ](?) ? rad (?) and d 2(a) ∈ rad (?) for all a ∈ ?. Finally, we characterize all pairs d, δ of continuous Φ-derivations such that dδ(a) is quasi-nilpotent for all a ∈ ? and [d, δ](?), [d, Φ](?), [δ,Φ](?) are subsets of rad (?). 相似文献
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Let R be a semiprime left Goldie ring with
a monomorphism and
an α-derivation, then
is semiprimitive left Goldie ring. 相似文献
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We consider hypercyclic composition operators on
which can be obtained from the translation operator using polynomial automorphisms of
. In particular we show that if C
S
is a hypercyclic operator for an affine automorphism S on
, then
for some polynomial automorphism Θ and vectors a and b, where I is the identity operator. Finally, we prove the hypercyclicity of “symmetric translations” on a space of symmetric analytic
functions on ℓ1.
Received: 8 June 2006 Revised: 26 September 2006 相似文献
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Jan Harm van der Walt 《Quaestiones Mathematicae》2016,39(2):167-178
The closed graph theorem is one of the cornerstones of linear functional analysis in Fréchet spaces, and the extension of this result to more general topological vector spaces is a di?cult problem comprising a great deal of technical difficulty. However, the theory of convergence vector spaces provides a natural framework for closed graph theorems. In this paper we use techniques from convergence vector space theory to prove a version of the closed graph theorem for order bounded operators on Archimedean vector lattices. This illustrates the usefulness of convergence spaces in dealing with problems in vector lattice theory, problems that may fail to be amenable to the usual Hausdorff-Kuratowski-Bourbaki concept of topology. 相似文献
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Asao Arai 《Integral Equations and Operator Theory》1995,21(2):139-173
LetA andB be two anticommuting self-adjoint operators andV() be a symmetric operator in a Hilbert space, where >0 is a parameter. It is proven that, under some conditions forV(), the resolvents of A+2
B±2|B|+V() converge as . Applications to the nonrelativistic-limit problem of Dirac operators and supersymmetry are discussed.This work is supported by the Grant-In-Aid 0560139 for science research from the Ministry of Education, Japan. 相似文献
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Asao Arai 《Integral Equations and Operator Theory》1993,16(1):38-63
LetA andB be anticommuting self-adjoint operators in a Hilbert space . It is proven thatiAB is essentially self-adjoint on a suitable domain and its closureC(A, B) anticommutes withA andB. LetU
s
be the partial isometry associated with the self-adjoint operatorsS, i.e., the partial isometry defined by the polar decompositionS=U
S
|S|. LetP
S
be the orthogonal projection onto (KerS). Then the following are proven: (i) The operatorsU
A
,U
B
,U
C(A,B)
,P
A
,P
B
, andP
A
P
B
multiplied by some constants satisfy a set of commutation relations, which may be regarded as an extension of that satisfied by the standard basis of the Lie algebra
of the special unitary groupSU(2); (ii) There exists a Lie algebra
associated with those operators; (iii) If is separable andA andB are injective, then
gives a completely reducible representation of
with each irreducible component being the spin representation of the Clifford algebra associated with 3; This result can be extended to the case whereA andB are not necessarily injective. Moreover, some properties ofA+B are discussed. The abstract results are applied to Dirac operators. 相似文献