Universal symbols on locally compact abelian groups

• Autorzy: Gorin E. A.
• Języki publikacji: EN

Abstrakty

EN

Let G be a locally compact abelian group, let X be its dual, let M(G) be the convolution algebra of all regular Borel measures of bounded variation on G, and let M (X) = {my | my is an element of M (G)}. A complex-valued function q on X is called symbol, if (the restriction) q|E is an element of M(X)|E for any compact subset E is a subset of X. If A is a Banach algebra then the group of invertible elements of A is denoted by A* and the spectral radius of a is an element of A is denoted by |a| . We consider continuous representations G is an element of g --> Tg is an element of A* such that ||Tg|| = 1 for all g is an element of G. In this case put my(T) = integral of GTg[my]dg). Obviously, we obtain a representation of M (G) (this representation is denoted by the same symbol T). It can easily be checked that hull(Ker(T)) is a subset of X. It leads to the correct definition of q(T) for all symbols q. Symbol q is called universal, if ||q(T)|| = |q(T)| for all T. The aim of the paper is to give a function-theoretic description of universal symbols.

Słowa kluczowe

EN

Banach algebra; spectrum; spectral radius; locally compact abelian groups; Bernstein's inequalities

PL

algebra Banacha; widmo; promień spektralny; grupa abelowa lokalnie zwarta; nierówność Bernsteina

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2003
• Tom: Vol. 51, no 2
• Strony: 199--204
• Opis fizyczny: Bibliogr. 1 poz.

Twórcy

autor

Gorin E. A.

• Moscow State Pedagogical University, Malaya Pirogovskaya str 1, 117 571, Moscow, Russia

Bibliografia

• [1] S. T. Norvidas, On the stability of differential operators in spaces of entire functions, Sov. Math. Dokl., 34 (3) (1986) 521-524; Original published in: Dokl. Akad. Nauk SSSR, 291 (3) (1986) 548-551 (in Russian).