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1.
It is shown that continuous -local derivations on -algebras are derivations and surjective -local *-automorphisms on prime -algebras or on -algebras such that the identity element is properly infinite are *-automorphisms.
2.
Let be a complex Hilbert space, be the algebra of all bounded linear operators on , be the subset of all selfadjoint operators in and or . Denote by the numerical radius of . We characterize surjective maps that satisfy for all without the linearity assumption.
3.
Bjö rn Schuster Nobuaki Yagita 《Proceedings of the American Mathematical Society》2004,132(4):1229-1239
We compute the Morava -theory of some extraspecial 2-groups and associated compact groups.
4.
Jerzy Kakol Stephen A. Saxon Aaron R. Todd 《Proceedings of the American Mathematical Society》2004,132(6):1703-1712
Let be a completely regular Hausdorff space, and let be the space of continuous real-valued functions on endowed with the compact-open topology. We find various equivalent conditions for to be a -space, resolving an old question of Jarchow and consolidating work by Jarchow, Mazon, McCoy and Todd. Included are analytic characterizations of pseudocompactness and an example that shows that, for , Grothendieck's -spaces do not coincide with Jarchow's -spaces. Any such example necessarily answers a thirty-year-old question on weak barrelledness properties for , our original motivation.
5.
Madjid Mirzavaziri Mohammad Sal Moslehian 《Proceedings of the American Mathematical Society》2006,134(11):3319-3327
Let be a -algebra acting on a Hilbert space , let be a linear mapping and let be a -derivation. Generalizing the celebrated theorem of Sakai, we prove that if is a continuous -mapping, then is automatically continuous. In addition, we show the converse is true in the sense that if is a continuous --derivation, then there exists a continuous linear mapping such that is a --derivation. The continuity of the so-called - -derivations is also discussed.
6.
Richard A. Shore 《Proceedings of the American Mathematical Society》2004,132(2):563-565
We give a short proof of the existence of minimal Turing degrees which are but not .
7.
For we give examples of Banach spaces isometrically embedding into but not into any with
8.
Sylvie Ruette 《Proceedings of the American Mathematical Society》2004,132(4):1091-1093
We show that there exist interval maps that are not Borel conjugate to any map. These examples can be chosen to be topologically mixing and , for any finite, arbitrarily large .
9.
John T. Anderson Alexander J. Izzo John Wermer 《Proceedings of the American Mathematical Society》2004,132(5):1495-1500
We prove: Let be a compact real-analytic variety in . Assume (i) is polynomially convex and (ii) every point of is a peak point for . Then . This generalizes a previous result of the authors on polynomial approximation on three-dimensional real-analytic submanifolds of .
10.
Huaxin Lin 《Proceedings of the American Mathematical Society》2004,132(11):3215-3224
Let be a non-unital and -unital simple -algebra. We show that if is simple, then is purely infinite. We also show that is simple if and only if has a continuous scale provided that is not isomorphic to the compact operators.
11.
Suppose that is a smooth -action on a closed smooth -dimensional manifold such that all Stiefel-Whitney classes of the tangent bundle to each connected component of the fixed point set vanish in positive dimension. This paper shows that if 2^k\dim F$"> and each -dimensional part possesses the linear independence property, then bounds equivariantly, and in particular, is the best possible upper bound of if is nonbounding.
12.
Gré gory Ginot Gilles Halbout 《Proceedings of the American Mathematical Society》2006,134(3):621-630
Let be the Hochschild complex of cochains on and let be the space of multivector fields on . In this paper we prove that given any -structure (i.e. Gerstenhaber algebra up to homotopy structure) on , and any -morphism (i.e. morphism of a commutative, associative algebra up to homotopy) between and , there exists a -morphism between and that restricts to . We also show that any -morphism (i.e. morphism of a Lie algebra up to homotopy), in particular the one constructed by Kontsevich, can be deformed into a -morphism, using Tamarkin's method for any -structure on . We also show that any two of such -morphisms are homotopic.
13.
James K. Deveney David R. Finston Peter van Rossum 《Proceedings of the American Mathematical Society》2004,132(10):2841-2848
Every locally trivial action of the additive group of complex numbers on four-dimensional complex affine space that is given by a triangular derivation is conjugate to a translation. A criterion for a proper action on complex affine -space to be locally trivial is given, along with an example showing that the hypotheses of the criterion are sharp.
14.
In this paper we consider the existence problem for the elliptic equation on , which arises in the study of conformal deformation of the hyperbolic disc. We prove an existence result for the above equation.
15.
Sergei V. Astashkin Lech Maligranda 《Proceedings of the American Mathematical Society》2004,132(10):2929-2938
We show that if is a rearrangement invariant space on that is an interpolation space between and and for which we have only a one-sided estimate of the Boyd index 1/p, 1 < p < \infty$">, then is an interpolation space between and . This gives a positive answer for a question posed by Semenov. We also present the one-sided interpolation theorem about operators of strong type and weak type .
16.
Shutao Chen Yunan Cui Henryk Hudzik 《Proceedings of the American Mathematical Society》2004,132(2):473-480
Criteria in order that an Orlicz space equipped with the Orlicz norm contains a linearly isometric copy (or an order linearly isometric copy) of (or ) are given.
17.
Martin Mathieu 《Proceedings of the American Mathematical Society》2004,132(2):443-446
A linear mapping from a subspace of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant such that for all , where denotes the spectral radius. We prove that every spectrally bounded unital operator from a unital purely infinite simple -algebra onto a unital semisimple Banach algebra is a Jordan epimorphism.
18.
Arne Ledet 《Proceedings of the American Mathematical Society》2004,132(9):2557-2561
We study the relationship between generic polynomials and generic extensions over a finite ground field, using dihedral extensions as an example.
19.
Toshihiro Shoda 《Proceedings of the American Mathematical Society》2004,132(5):1285-1293
A complete oriented stable minimal surface in is a plane, but in , there are many non-flat examples such as holomorphic curves. The Gauss map plays an important role in the theory of minimal surfaces. In this paper, we prove that a complete oriented stable minimal surface in with -degenerate Gauss map (for 1/4$">) is a plane.
20.
Theodore A. Slaman 《Proceedings of the American Mathematical Society》2004,132(8):2449-2456
Working in the base theory of , we show that for all , the bounding principle for -formulas ( ) is equivalent to the induction principle for -formulas ( ). This partially answers a question of J. Paris.