相关论文: Projective limit of a sequence of compatible weak …

Given an ascending sequence of weak symplectic Banach manifolds on which the Darboux theorem is true, we can ask about conditions under which the Darboux Theorem is also true on the direct limit. We will show in general, without very strong…

Suppose M be the projective limit of weak symplectic Banach manifolds \{(M_i,\phi_{ij})\}_{i,j\in\mathbb N}, where M_i are modeled over reflexive Banach space and \sigma is compatible with the inverse system(defined in the article). We…

We provide sufficient conditions for the existence of Darboux charts on weakly symplectic bounded Fr\'{e}chet manifolds by using the Moser's trick.

We give an integrability criterion for a projective limit of Banach distributions on a Fr\'echet manifold which is a projective limit of Banach manifolds. This leads to a result of integrability of projective limit of involutive bundles on…

It is shown that if a Banach space X has the weak Banach-Saks property and the weak fixed point property for nonexpansive mappings and Y satisfies property asymptotic (P) (which is weaker than the condition WCS(Y)>1), then the direct sum of…

The Darboux theorem in symplectic geometry implies that any two points in a connected symplectic manifold have neighbourhoods symplectomorphic to each other. The impossibility of such a theorem in the more general multisymplectic framework…

Using the game approach to fragmentability, we give new and simpler proofs of the following known results: (a) If the Banach space admits an equivalent Kadec norm, then its weak topology is fragmented by a metric which is stronger than the…

For a finite dimensional symplectic manifold $(M,\omega)$ with a symplectic form $\omega$, corresponding loop space ($LM=C^\infty(S^1,M)$) admits a weak symplectic form $\Omega^\omega$. We prove that the loop space over $\mbr^n$ admits…

Recently, extending work by Karshon, Kessler and Pinsonnault, Borisov and McDuff showed that a given symplectic manifold $(M,\omega)$ has a finite number of distinct toric structures. Moreover, McDuff also showed a product of two projective…

Let $\{X, X_{n}; n \geq 1 \}$ be a sequence of i.i.d. $\mathbf{B}$-valued random variables and set $S_{n} = \sum_{i=1}^{n}X_{i},~n \geq 1$. This note is devoted to study the classical central limitr theorem for subsequences of sums of…

We define the notion of strong projective limit of Banach Lie algebroids. We study the associated structures of Fr\'{e}chet bundles and the compatibility with the different morphisms. This kind of structure seems to be a convenient…

In this paper, we prove some theorems related to properties of generalized symmetric hybrid mappings in Banach spaces. Using Banach limits, we prove a fixed point theorem for symmetric generalized hybrid mappings in Banach spaces. Moreover,…

It is shown that certain lower semi-continuous maps from a paracompact space to the family of closed subsets of the bundle space of a Banach bundle admit continuous selections. This generalization of the theorem of Douady, dal…

A singular Moishezon space is not projective even if it is Kaehler. This paper gives a projectivity criterion for Kaehler Moishezon spaces. We shall use this projectivity criterion to show the density of projective symplectic varieties in…

We introduce Morse-type inequalities for a holomorphic circle action on a holomorphic vector bundle over a compact Kaehler manifold. Our inequalities produce bounds on the multiplicities of weights occurring in the twisted Dolbeault…

Let k be a number field. For a variety X over k that satisfies weak approximation with Brauer-Manin obstruction, we study the same property for smooth projective models of its symmetric products. Based on the same method, we also explore…

We provide sufficient conditions for a Banach space Y to be weakly sequentially complete. These conditions are expressed in terms of the existence of directional derivatives for cone convex mappings with values in Y .

A boundary for a Banach space is a subset of the dual unit sphere with the property that each element of the Banach space attains its norm on an element of that subset. Trivially, the pointwise convergence with respect to such a boundary is…

We give a sufficient condition for a pair of Banach spaces $(X,Y)$ to have the following property: whenever $W_1 \subseteq X$ and $W_2 \subseteq Y$ are sets such that $\{x\otimes y: \, x\in W_1, \, y\in W_2\}$ is weakly precompact in the…

We consider all complex projective manifolds X that satisfy at least one of the following three conditions: 1. There exists a pair $(C ,\varphi)$, where $C$ is a compact connected Riemann surface and $\varphi : C\to X$ a holomorphic map,…