Analytic functionals on the Wiener space

We define the analyticity of Wiener functionals and study its properties and applications to oscillatory Wiener functionals. Project supported by the National Natural Science Foundation of China.     

Linear maps that preserve matrices annihilated by a polynomial

Let M_n be the algebra of n×n matrices over an algebraically closed field of characteristic zero. Let f(x) be a polynomial over $\text{F}$ with at least two distinct roots. Then all nonsingular linear maps L:M_n→M_n that map matrix roots of F(x)=0 into matrix roots of f(x}=0 are found.     

Analytic deviation of ideals and intersection theory of analytic spaces

In this note a stratification of analytic subspaces by analytic deviation of ideals is introduced and applied to define embedded components of an intersection (not necessarily proper) of complex analytic subspaces. Using the method of compact semi-analytic Stein neighbourhoods, a pointwise defined intersection multiplicity is proved to be constant along a dense Zariski open subset of such embedded components. For complex subspaces of a projective space one obtains precisely the distinguished varieties of intersection in the sense of Fulton and their intersection numbers.     

Linear maps on operator algebras that preserve elements annihilated by a polynomial

In this paper some purely algebraic results are given concerning linear maps on algebras which preserve elements annihilated by a polynomial of degree greater than 1 and with no repeated roots and applied to linear maps on operator algebras such as standard operator algebras, von Neumann algebras and Banach algebras. Several results are obtained that characterize such linear maps in terms of homomorphisms, anti-homomorphisms, or, at least, Jordan homomorphisms.

     

Multiplier ideals of monomial ideals

In this note we discuss a simple algebraic calculation of the multiplier ideal associated to a monomial ideal in affine -space. We indicate how this result allows one to compute not only the multiplier ideal but also the log canonical threshold of an ideal in terms of its Newton polygon.

     

Factorization of injective ideals by interpolation

We construct a factorization of certain multilinear mappings through linear operators belonging to closed, injective operator ideals using interpolation technique. An extension of the duality theorem for interpolation spaces is also obtained.     

Associated radical ideals of monomial ideals

Algebraic and combinatorial properties of a monomial ideal are studied in terms of its associated radical ideals. In particular, we present some applications to the symbolic powers of square-free monomial ideals.     

Principal Borel ideals and Gotzmann ideals

In this paper we characterize all principal Borel ideals with Borel generator up to degree 4 which are Gotzmann. We also classify principal Borel ideals with a Borel generator of degree d which are lexsegment and we describe the shadows of principal Borel ideals. Finally, we discuss the corresponding results for squarefree monomial ideals.Received: 10 May 2002     

Decomposition of ideals into pseudo-irreducible ideals

A proper ideal of a commutative ring is called pseudo-irreducible if it cannot be written as a product of two comaximal proper ideals. In this paper, we give a necessary and su?cient condition for every proper ideal of a commutative ring to be a product of pairwise comaximal pseudo-irreducible ideals. Examples of such rings include Laskerian rings, or more generally J-Noetherian rings and ZD-rings. We study when certain classes of rings satisfy this condition.     

The approximation properties determined by operator ideals

We introduce the notion of the right approximation property with respect to an operator ideal A and solve the duality problem for the approximation property with respect to an operator ideal A, that is, a Banach space X has the approximation property with respect to A ^d whenever X* has the right approximation property with respect to an operator ideal A. The notions of the left bounded approximation property and the left weak bounded approximation property for a Banach operator ideal are introduced and new symmetric results are obtained. Finally, the notions of the p-compact sets and the p-approximation property are extended to arbitrary Banach operator ideals. Known results of the approximation property with respect to an operator ideal and the p-approximation property are generalized.