On the norm of an idempotent Schur multiplier on the Schatten class

We show that if the norm of an idempotent Schur multiplier on the Schatten class lies sufficiently close to , then it is necessarily equal to . We also give a simple characterization of those idempotent Schur multipliers on whose norm is .

     

Inverse-Definiteness of the Fourth-Order Symmetric Differential Operator （Ⅰ）

Abstract   We give a linear symmetric differential operator L defined by

A Littlewood-Paley type inequality

In this note we prove the following theorem: Let u be a harmonic function in the unit ball and . Then there is a constant C = C(p, n) such that

Effective syntheses of quinoline-7,8-diol, 5-amino-l-DOPA, and 3-(7,8-dihydroxyquinolin-5-yl)-l-alanine

A modification of the Baeyer-Villiger reaction allows the conversion of aromatic 2-hydroxy-3-nitroketones and aldehydes into 3-nitrocatechols, which can be reduced to 3-aminocatechols. Reaction of the latter with acrolein yields quinoline-7,8-diols under exceptionally mild conditions. This new reaction sequence was successfully applied to the synthesis of the title compounds.     

On a generalised<Emphasis Type="Italic">ε</Emphasis>-control problem in Banach space

In this paper a linearε-control problem for a general objective function is considered by functional analytic approach. Existence and uniqueness of solutions are shown. The characterization of the solution is given in terms of a hyperplane.     

On the structure of inner ideals of nest algebras

IfA is a nest algebra andA _s=A ∩ A* , whereA* is the set of the adjoints of the operators lying inA, then the pair (A, A _s) forms a partial Jordan *-triple. Important tools when investigating the structure of a partial Jordan *-triple are its tripotents. In particular, given an orthogonal family of tripotents of the partial Jordan *-triple (A, A _s), the nest algebraA splits into a direct sum of subspaces known as the Peirce decomposition relative to that family. In this paper, the Peirce decomposition relative to an orthogonal family of minimal tripotents is used to investigate the structure of the inner ideals of (A, A _s), whereA is a nest algebra associated with an atomic nest. A property enjoyed by inner ideals of the partial Jordan *-triple (A, A _s) is presented as the main theorem. This result is then applied in the final part of the paper to provide examples of inner ideals. A characterization of the minimal tripotents as a certain class of rank one operators is also obtained as a means to deduce the principal theorem.     

Some remarks on half-factorial orders

In questo articolo, si dimostra il legame fra la semi-fattorialità e la fattorialità debole nel contesto degli ordini algebrici. In particolare, si ottiene che un ordine semi-fattoriale ha il stesso numero di classi che su chiusura integrale.     

Bounded point evaluations and cyclic polynomials on the spaces $$\hat F$$

LetF be aBK space withAK and denote the set of all formal power series with such that ε F for the sequence of coefficients of . We give a necessary and sufficient condition for a point to be a bounded point evaluation on , and for a polynomial to be cyclic in . As special cases, we obtain the results for the space ℓ _p (β) in [7]. Research of the authors supported under the research project #1232 of the Serbian Ministry of Sciences and Tecnology and, in the case of the second author, also by the DAAD foundation (German Academic Exchange Service), grant 911 103 102 8.