Showing papers by "Chung Yuan Christian University published in 1985"

The unitary equivalence of compact operators

Abstract: The problem of determining whether or not two operators are unitarily equivalent has been around for many years and considerable work has been done in attempting to solve this problem (see for example [1], [3], [5], [6], [7], [10], [11], [12], [15], [16], [17], [18], [19], [20], [21] and [22]). In many cases, a complete set of unitary invariants is furnished for a certain class of operators. Here we just mention two of such results which are related to what we are going to discuss. The first one was due to Arveson, who showed that two irreducible compact operators are unitarily equivalent if and only if they have the same nth algebraic matricial ranges, for each n ≧1 ([1] and Theorem 2.4.3 of [3]). The second one was due to Parrott, who showed that two compact operators with zero reducing null spaces are unitarily equivalent if and only if they have the same nth spatial matricial ranges, for each n ≧1 ([5, p. 146]). In this paper, we investigate the closures of the spatial matricial ranges of compact operators and obtain a complete set of unitary invariants for compact operators, from which Parrott's result follows easily.

Factorizations in a semigroup of integral matrices

Abstract: This paper is devoted to the study of the factorization of elements of the multiplicative semigroup. of two-by-two matrices with positive integral entries and of determinant one. All the primes are identified. It is shown that there are two canonical ways to factorize the composites of into products of primes and these two canonical prime factorizations consist of the same number of factors. As an application of this theory of factorization the automorphisms and anti-automorphisms on are determined.

Direct synthesis of aromatic polyesters by use of a sulfonium salt derived from tosyl chloride and N-methylimidazole

Abstract: A sulfonium salt derived from tosyl chloride and N-methylimidazole was successfully used as an effective condensing agent for the preparation of high-molecular-weight aromatic polyesters by the direct polycondensation of aromatic dicarboxylic acids and bisphenols. Conditions for the formation of the sulfonium salt and of the reaction of the salt with dicarboxylic acids favorable for the polycondensation were examined. Thermal property of a polymer was investigated in terms of random sequences of monomer in the polymer backbone. Preparation of a polyamide and a polyesteramide was attempted with limited success.

Preparation of aromatic copolyesteramides by the direct polycondensation with a vilsmeier adduct derived from tosyl chloride and N,N‐dimethylformamide

Abstract: The reaction promoted by Vilsmeier adduct derived from tosyl chloride (TsCl) with N,N-dimethylformamide (DMF) was successfully applied to the preparation of copolyesteramides of high molecular weights directly from aromatic dicarboxylic acids, diamines, and bisphenols. The polycondensation was significantly affected by the reaction of activated dicarboxylic acids with bisphenols and diamines. Addition of a mixture of bisphenols and diamines likely caused gelation of the reaction mixtures, resulting in insoluble polymers, especially with high mol % diamines. Stepweise addition of them, however, gave the homogeneous reaction mixtures and copolymers of better solubility. These phenomena were studied in terms of sequence length distribution of polyester units, which was estimated by thermal analyses of the random copolymers prepared under various conditions for the initial reaction with bisphenols.