We prove that every maximal coonitary group has size at least the cardinality of the smallest non{meager set of reals. We also provide a consistency result saying that the spectrum of possible cardinalities of maximal coonitary groups may be quite arbitrary.

Let G denote a locally compact abelian topological group (an l.c.a. group) with dual group C\ We will denote by A7(G) the Banach algebra of bounded regular Borel measures on G under convolution multiplication and by L(G) the algebra of bounded measures absolutely continuous with respect to Haar measure on G (for discussions of these Banach algebras cf. [1], [2], and [5]). In this paper we shall...

(Here ΛE is a suitable period lattice commensurable with the Néron lattice of E.) The function Φ, which is transcendental as a function of τ , enjoys the following notable algebraicity property, a consequence of the theory of complex multiplication: Theorem HP: Let K ⊂ C be a quadratic imaginary extension of Q, and let K denote its maximal abelian extension. If τ belongs to H ∩ K, then Φ(τ) bel...

In this paper, we introduce and analyze some generalized hybrid proximal point algorithms for finding a common element of the set of zeros of a maximal monotone operator and the set of fixed points of a nonexpansive mapping in a Hilbert space. These algorithms include the previously known proximal point algorithms as special cases. Weak and strong convergence of the proposed proximal point algo...

In addition to Pisier’s counterexample of a non-accessible maximal Banach ideal, we will give a large class of maximal Banach ideals which are accessible. The first step is implied by the observation that a ”good behaviour” of trace duality, which is canonically induced by conjugate operator ideals can be extended to adjoint Banach ideals, if and only if these adjoint ideals satisfy an accessib...