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1.
M. Fragoulopoulou 《Periodica Mathematica Hungarica》1988,19(3):181-208
V. Pták's inequality is valid for every hermitian completeQ locallym-convex (:l.m.c.) algebra. Every algebra of the last kind is, in particular, symmetric. Besides, a (Hausdorff) locallyC
*-algebra (being always symmetric) with the propertyQ is, within a topological algebraic isomorphism, aC
*-algebra. Furthermore, a type of Raikov's criterion for symmetry is also valid for non-normed topological*-algebras. Concerning topological tensor products, one gets that symmetry of the-completed tensor product of two unital Fréchet l.m.c.*-algebrasE, F ( denotes the projective tensorial topology) is always passed toE, F, while the converse occurs when moreover either ofE, F is commutative. 相似文献
2.
M. Fragoulopoulou 《Periodica Mathematica Hungarica》1986,17(3):185-209
An advertibly complete locallym-convex (lmc)*-algebraE is symmetric if and only if each normed (inverse limit) factorE/N
, A, ofE is symmetric in the respective Banach factorE
, A, ofE. Every locally C*-algebra is symmetric. If denotes the continuous positive functionals on an lmc*-algebraE and withL
f
={x E: f(x
*
x) =0}, thenE is, by definition,-commutative if for anyx, y E.-commutativity and commutativity coincide in lmcC
*-algebras, so that an lmc*-algebra with a bounded approximate identity is-commutative if and only if its enveloping algebra is commutative. Several standard results for commutative lmc*-algebras are also obtained in the-commutative case, as for instance, the nonemptiness of the Gel'fand space of a suitable-commutative lmc*-algebra, the automatic continuity of positive functionals when the algebras involved factor, as well as that the spectral radius is a continuous submultiplicative semi-norm, when the algebras considered are moreover symmetric. An application of the latter result yields a spectral characterization of-commutativity. 相似文献
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We discuss the representation theory of both the locally convex and non-locally convex topological*-algebras. First we discuss the*-representation of topological*-algebras by operators on a Hilbert space. Then we study those topological*-algebras so that every*-representation of which on a Hilbert space is necessarily continuous. It is well-known that each*-representation of aB
*-algebra on a Hilbert space is continuous. We show that this is true for a large class of*-algebras more general thanB
*-algebras, including certain non-locally convex*-algebras. Finally, we investigate the conditions under which a positive functional on a topological*-algebra is representable.The research of the first-named author was partially supported by an NSERC grant. This work was done by the second-named author when he was a post-doctoral fellow at McMaster University. 相似文献
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David L Johnson 《Journal of Mathematical Analysis and Applications》1982,89(2):359-369
It is shown that the set m × n of complex m × n matrices forms a lower semilattice under the partial ordering A ? B defined by denotes the conjugate transpose of A. As a special case of a result for division rings, it is further shown that, over any field F, form = n = 2 and any proper involution 1 of F2 × 2, the corresponding intersections A ∩ B all exist. 相似文献
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A new class of locally convex algebras, called BP*-algebras, is introduced. It is shown that this class properly includes MQ*-algebras which were introduced and studied by the first author andR. Rigelhof [10]. Among other results, it is proved that each positive functional on a BP*-algebraA is admissible but not necessarily continuous as shown by an example. However, ifA, in addition, is either (i) a Q-algebra, or (ii) has an identity and is barrelled, or (iii)A is endowed with the inductive limit topology, then each positive functional onA is continuous.This work was supported by an N.R.C. Grant. 相似文献
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Mohammad Gholampour 《Quaestiones Mathematicae》2018,41(2):227-238
We prove that every generalized Jordan derivation D from a JB?-algebra 𝒜 into itself or into its dual space is automatically continuous. In particular, we establish that every generalized Jordan derivation from a C?-algebra to a Jordan Banach module is continuous. As a consequence, every generalized derivation from a C?-algebra to a Banach bimodule is continuous. 相似文献
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Z. Sebestyén 《Periodica Mathematica Hungarica》1986,17(4):247-254
14.
Silvia ScĂrlĂtescu-Murea 《Rendiconti del Circolo Matematico di Palermo》2000,49(3):561-574
This paper is concerned with the connection between the structure space of a locally C*-algebra and the set of its continuous
topologically irreducible *-representations. Properties of primitive ideals in such algebras are further investigated, for
instance, closed ideals are expressed as intersections of primitive ideals, by using that the Jacobson radical reduces to
0. 相似文献
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Unbounded C*-seminorms generated by families of biweights on a partial *-algebra are considered and the admissibility of biweights
is characterized in terms of unbounded C*-seminorms they generate. Furthermore, it is shown that, under suitable assumptions,
when the family of biweights consists of all those ones which are relatively bounded with respect to a given C*-seminorm q, it can be obtained an expression for q analogous to that one which holds true for the norm of a C*-algebra. 相似文献
17.
C. T. Tucker 《Periodica Mathematica Hungarica》1984,15(4):253-257
An ordered linear spaceL is said to satisfy extension property (E1) if for every directed subspaceM ofL and positive linear functional ϕ onM, ϕ can be extended toL.
A Riesz spaceL is said to satisfy extension property (E2) if for every sub-Riesz spaceM ofL and every real valued Riesz homomorphism ϕ onM, ϕ can be extended toL as a Riesz homomorphism.
These properties were introduced by Schmidt in [5].
In this paper, it is shown that an ordered linear space has extension property (E1) if and only if it is order isomorphic
to a function spaceL′ defined on a setX′ such that iff andg belong toL′ there exists a finite disjoint subsetM of the set of functions onX′ such that each off andg is a linear combination of the points ofM.
An analogous theorem is derived for Riesz spaces with extension property (E2). 相似文献
18.
B. Zalar 《Aequationes Mathematicae》1997,54(1-2):31-43
Summary We give a new simple proof of Šemrl’s recent representation theorem for quasi-quadratic functions acting on unital modules
and then show that our approach also gives a certain extension of Šemrl’s result.
This paper is intended to point out the usefulness of the ternary point of view even when we are dealing with problems which
involve only binary structure.
Dedicated to the memory of Professor Gy?rgy Szabó
Supported in part by the Slovene Ministry of Science grant P1-5505-0101/93. 相似文献
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Jean-Pierre Antoine Camillo Trapani Francesco Tschinke 《Mediterranean Journal of Mathematics》2007,4(3):357-373
We continue the study of Banach partial *-algebras, in particular the question of the interplay between *-homomorphisms and
biweights. Two special types of objects are introduced, namely, relatively bounded biweights and Banach partial *-algebras
satisfying a certain Condition (S), which behave in a more regular way. We also present a systematic construction of Banach
partial *-algebras of this type and exhibit several examples. 相似文献