We show that the matricial norms of a non-unital operator algebra determine those of the algebra obtained by adjoining a unit to it. As applications , we classify two-dimensional unital operator algebras and show that the algebra of bounded holomorphic functions on a strongly pseudoconvex domain has a contractive representation that is not completely contractive.

Recently Daniel and Palmer [2J have given an interesting application of a little-known lemma due to A. E. Taylor** [3J concerning the existence of an "orthogonal" basis for a finite dimensional (real or complex) normed vector space. Here we shall apply Taylor's lemma to obtain some simple results which have apparently not been noticed before. Thus we shall show that, given any bound norm (3, we...

A C-metric algebra consists of a unital C-algebra and a Leibniz Lip-norm on the C-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital -homomorphism from a C-metric algebra to another one is necessarily Lipschitz. It results that the free product of two Lipschitz unital -homomorphisms between C-metric algebras coming from -filtrations is still a Lipschitz u...

We prove comparison theorems for norms of iteration matrices in splittings of matrices in the setting of proper cones in a finite dimensional real space by considering cone linear absolute norms and cone max norms. Subject to mild additional hypotheses, we show that these comparison theorems can hold only for such norms within the class of cone absolute norms. Finally, in a Banach algebra setti...

We present the basic analytical and algebraic properties of triangular norms. We discuss continuity as well as the important classes of Archimedean, strict and nilpotent t-norms. Triangular conorms and De Morgan triples are also mentioned. Finally, a brief historical survey on triangular norms is given. Submitted for publication Johannes Kepler Universität Linz Fuzzy Logic Laboratorium Linz-Hag...

Left-continuity of triangular norms is the characteristic property to make it a residuated lattice. Nowadays residuated lattices are subjects of intense investigation in the ÿelds of universal algebra and nonclassical logic. The recently known construction methods resulting in left-continuous triangular norms are surveyed in this paper.

Triangular norms, or t-norms for short, play an important role for the semantics of fuzzy logics. Although an enormous number of examples and a remarkable number of construction methods for this kind of operation has been established, a uniform approach is still outstanding. This paper is devoted to a specific algebraic-geometrical framework within which t-norms, up to isomorphism, can be descr...