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Marcus Carlsson 《Integral Equations and Operator Theory》2008,61(4):593-598
In [3], M. J. Cowen and R. G. Douglas prove that the adjoint of a Hilbert space operator T is in the class if and only if T is unitarily equivalent with the operator M
z
on a Hilbert space -valued analytic functions, where M
z
denotes the operator of multiplication by the independent variable. The proof involves holomorphic vector bundles and Grauert’s
theorem.
In this paper we use a theorem by I. Gohberg and L. Rodman [4] to give a more elementary proof of this fact, which also works
for Banach space operators.
相似文献
3.
In this paper, we compute certain invariants of extension algebras of the torus algebra by , where is the C*-algebra of compact operators on an infinite dimensional separable Hilbert space H. These extension algebras are also constructed up to isomorphism.
Received: 5 July 2007, Revised: 14 February 2008 相似文献
4.
In this article we study certain functional equations and systems of functional equations related to (generalized) derivations
on semiprime rings. In particular, we prove that any generalized Jordan triple derivation on a 2- torsion free semiprime ring
is a generalized derivation. We also prove that any (generalized) Jordan triple *-derivation on a 2-torsion free semiprime
*-ring is a (generalized) Jordan *-derivation.
The second author was supported in part by the Ministry of Science, Education and Sports of the Republic of Croatia (project
No. 037-0372784-2757). 相似文献
5.
Sorin Dăscălescu 《Archiv der Mathematik》2008,91(3):212-217
We describe all group gradings on the diagonal algebra k
n
, where k is an arbitrary field.
Received: 21 January 2008 相似文献
6.
Wen-Kwei Shiue 《Rendiconti del Circolo Matematico di Palermo》2003,52(3):505-509
LetR a prime ring,L a noncentral Lie ideal ofR anda ∈R. Suppose thatd is a nonzero derivation ofR such thata[d(u),u]
k
=0 for allu ∈L, wherek is a fixed positive integer. Thena=0 except when charR=2 and dim
C
RC=4. 相似文献
7.
This paper deals with the automatic continuity theory for the convolution algebra of all Bochner integrable functions from
a locally compact abelian group G into an arbitrary unital complex Banach algebra A. For non-compact G, it is shown that all epimorphisms and all derivations on this vector-valued group algebra are necessarily continuous while
for compact G, such results depend heavily on the automatic continuity properties of the range algebra a.
Dedicated to Heinz Konig on the occasion of his 65th birthday
Research supported by Grant SNF 11-1015 from the Danish Science Research Council. 相似文献
8.
Elói Medina Galego 《Archiv der Mathematik》2007,88(1):52-56
Let X and Y be Banach spaces such that each of them is isomorphic to a complemented subspace of the other. In 1996, W. T. Gowers solved
the Schroeder-Bernstein problem for Banach spaces by showing that X is not necessarily isomorphic to Y . Let (p, q, r, s) be a quadruple in
with p + q ≥ 2 and r + s ≥ 2. Suppose that for every pair of Banach spaces X and Y isomorphic to complemented subspaces of each other and satisfying the following Decomposition Scheme
we conclude that Xm is isomorphic to Yn for some
. In this paper, we show that the discriminant
of this quadruple is different from zero. This result completes the characterization of quadruples in
which are nearly Schroeder-Bernstein Quadruples for Banach spaces.
Received: 10 September 2005 相似文献
9.
M. Hemdaoui 《Rendiconti del Circolo Matematico di Palermo》2006,55(1):140-146
In this note, we show that it is possible to define vectorial powers of some elements in unital complex Banach algebras. 相似文献
10.
Teresa Bermúdez Isabel Marrero Antonio Martinón 《Integral Equations and Operator Theory》2009,64(4):487-494
A bounded linear operator T on a Hilbert space H is called an m-isometry for a positive integer m if . We prove some properties concerning the behaviour of the orbit of an m-isometry. For example, every orbit of an m-isometry is eventually norm increasing and some m-isometries can not be N-supercyclic, that is, there does not exist an N-dimensional subspace EN such that the orbit of T at EN is dense in H.
To Professor José Rodríguez Expósito on his 60th birthday 相似文献
11.
It was once conjectured that if A is a uniform algebra on its maximal ideal space X, and if each point of X is a peak point for A, then A = C(X). This peak point conjecture was disproved by Brian Cole in 1968. However, Anderson and Izzo showed that the peak point conjecture
does hold for uniform algebras generated by smooth functions on smooth two-manifolds with boundary. The corresponding assertion
for smooth three-manifolds is false, but Anderson, Izzo, and Wermer established a peak point theorem for polynomial approximation
on real-analytic three-manifolds with boundary. Here we establish a more general peak point theorem for real-analytic three-manifolds
with boundary analogous to the two-dimensional result. We also show that if A is a counterexample to the peak point conjecture generated by smooth functions on a manifold of arbitrary dimension, then
the essential set for A has empty interior. 相似文献
12.
We present the development of the Lucid language from the Original Lucid of the mid-1970s to the TransLucid of today. Each
successive version of the language has been a generalisation of previous languages, but with a further understanding of the
problems at hand.
The Original Lucid (1976), originally designed for purposes of formal verification, was used to formalise the iteration in
while-loop programs. The pLucid language (1982) was used to describe dataflow networks. Indexical Lucid (1987) was introduced for
intensional programming, in which the semantics of a variable was understood as a function from a universe of possible worlds
to ordinary values. With TransLucid, and the use of contexts as firstclass values, programming can be understood in a Cartesian
framework.
相似文献
13.
The first author introduced an integration theory of vector functions with respect to an operator-valued measure in complete
bornological locally convex vector spaces. In this paper some important results behind this Dobrakov-type integration technique
in non-metrizable spaces are given.
Received: December 10, 2007., Accepted: May 6, 2008. 相似文献
14.
If the unit sphere of a Banach space X can be covered by countably many balls no one of which contains the origin, then, as an easy consequence of the separation
theorem, X* is w*-separable. We prove the converse under suitable renorming. Moreover, the balls of the countable covering can be chosen as
translates of the same ball.
Research of V. P. Fonf was supported in part by Israel Science Foundation, Grant # 139/02 and by the Istituto Nazionale di
Alta Matematica of Italy. Research of C. Zanco was supported in part by the Ministero dell’Università e della Ricerca Scientifica
e Tecnologica of Italy and by the Center for Advanced Studies in Mathematics at the Ben-Gurion University of the Negev, Beer-Sheva,
Israel. 相似文献
15.
Gilles Godefroy 《Archiv der Mathematik》2009,92(5):476-484
Our main result shows that subspaces of L1([0, 1]) on which the blow-up operators act compactly are isometric to dual spaces, and their natural predual belongs to the
Banach-Mazur closure of quotient spaces of . Related general results are shown for subspaces X of or of reflexive K?the function spaces, which imply that when X consists of smooth functions it embeds into a Banach space with an unconditional basis.
Received: 25 September 2008 相似文献
16.
Glyn Harman 《Archiv der Mathematik》2008,90(3):239-245
Let P
+(m) denote the greatest prime factor of the positive integer m. Improving and simplifying work of Dartyge [3] we show that
for . Here improves on the previous exponent .
Received: 20 April 2007 相似文献
17.
Two classes of Banach algebras which admit a matrix symbol of order 2 are described, and an explicit form of the symbol is obtained. Also we describe all polynomialsF(X, Y) andF(X, Y, Z) such that the norms of polynomialsF(B, B
*) (whenB
2=0) andF(S, W, W
*
) (whenS
2
=I, W
2
=0, S
*=S) depend only on the polynomialF and on the norms B, W. Applications to Banach algebras generated by singular integral operators and some their perturbations are considered. 相似文献
18.
Matthew Towers 《Archiv der Mathematik》2009,92(3):215-227
Let G be a finite p-group with subgroup H and k a field of characteristic p. We study the endomorphism algebra E = EndkG(kH ↑G), showing that it is a split extension of a nilpotent ideal by the group algebra kNG(H)/H. We identify the space of endomorphisms that factor through a projective kG-module and hence the endomorphism ring of kH ↑G in the stable module category, and determine the Loewy structure of E when G has nilpotency class 2 and [G, H] is cyclic.
Received: 3 November 2008 相似文献
19.
It is observed that the additive as well as multiplicative Jordan decompositions hold in alternative loop algebras of finiteRA loops and theRA loops for which the additive Jordan decomposition holds in the integral loop ring are characterized. Multiplicative Jordan
decomposition (MJD) inZL, whereL is a finiteRA loop with cyclic centre is analysed, besides settling MJD for integral loop rings of allRA loops of order ≤32. It is also shown that for any finiteRA loopL,U
(ZL) is an almost splittable Moufang loop.
Research of the second author is supported by CSIR. 相似文献
20.