Partitions of spectral sets
P-commutativity of the Banach Algebra L1 (G).
Peak Points for Algebras on Circled Sets.
Pervasive algebras and maximal subalgebras
A uniform algebra A on its Shilov boundary X is maximal if A is not C(X) and no uniform algebra is strictly contained between A and C(X). It is essentially pervasive if A is dense in C(F) whenever F is a proper closed subset of the essential set of A. If A is maximal, then it is essentially pervasive and proper. We explore the gap between these two concepts. We show: (1) If A is pervasive and proper, and has a nonconstant unimodular element, then A contains an infinite descending chain of pervasive...
Pervasive algebras on planar compacts
We characterize compact sets in the Riemann sphere not separating for which the algebra of all functions continuous on and holomorphic on , restricted to the set , is pervasive on .
Picard's theorem, Mittag-Leffler methods, and continuity of characters on Fréchet algebras
Pick interpolation for a uniform algebra
Podal subspaces on the unit polydisk
Beurling's classical theorem gives a complete characterization of all invariant subspaces in the Hardy space H²(D). To generalize the theorem to higher dimensions, one is naturally led to determining the structure of each unitary equivalence (resp. similarity) class. This, in turn, requires finding podal (resp. s-podal) points in unitary (resp. similarity) orbits. In this note, we find that H-outer (resp. G-outer) functions play an important role in finding podal (resp. s-podal) points. By the methods...
Point derivations and prime ideals in R(X)
Point derivations on algebraic extension of Banach algebra.
Pointwise multiplication operators on weighted Banach spaces of analytic functions
For a wide class of weights we find the approximative point spectrum and the essential spectrum of the pointwise multiplication operator , , on the weighted Banach spaces of analytic functions on the disc with the sup-norm. Thus we characterize when is Fredholm or is an into isomorphism. We also study cyclic phenomena for the adjoint map .
Polynomial identification in uniform and operator algebras.
Positive multiplication preserves dissipativity in commutative -algebras.
Positive-definite kernels, length functions on groups and a noncommutative von Neumann inequality
Power boundedness in Banach algebras associated with locally compact groups
Let G be a locally compact group and B(G) the Fourier-Stieltjes algebra of G. Pursuing our investigations of power bounded elements in B(G), we study the extension property for power bounded elements and discuss the structure of closed sets in the coset ring of G which appear as 1-sets of power bounded elements. We also show that L¹-algebras of noncompact motion groups and of noncompact IN-groups with polynomial growth do not share the so-called power boundedness property. Finally, we give a characterization...
Power series developments in lattice ordered semigroups.
Power-bounded elements and radical Banach algebras
Firstly, we give extensions of results of Gelfand, Esterle and Katznelson--Tzafriri on power-bounded operators. Secondly, some results and questions relating to power-bounded elements in the unitization of a commutative radical Banach algebra are discussed.
Primary Ideals in Beurling Algebras.
Principalité des idéaux de type fini de
Problèmes de complémentation de sous-algèbres dans l'algèbre des séries de Fourier en deux variables absolument convergentes