相关论文: Iwasawa decompositions of some infinite-dimensiona…

We proof some basic tools about spaces of H"older-continuous functions between (in general infinite dimensional) Banach spaces and use them to construct new examples of infinite dimensional (LB)-Lie groups.

The Cartan and Iwasawa decompositions of real reductive Lie groups play a fundamental role in the representation theory of the groups and their corresponding symmetric spaces. These decompositions are defined by an involution with a compact…

For locally convex, nilpotent Lie algebras we construct faithful representations by nilpotent operators on a suitable locally convex space. In the special case of nilpotent Banach-Lie algebras we get norm continuous representations by…

We show that the superanalogue of the Iwasawa decomposition exists for supergroup $SL(n,m,\mathbb{C})$. The first component of the decomposition is the compact real form $SU(n,m)$, which was constructed following the idea of our article…

Let $H=H_+\oplus H_-$ be a fixed orthogonal decomposition of the complex Hilbert space $H$ in two infinite dimensional subspaces. We study the geometry of the set $P^p$ of selfadjoint projections in the Banach algebra $$ {\cal A}^p=\{A\in…

Let $K_\infty/K$ be a uniform $p$-adic Lie extension. We compare several arithmetic invariants of Iwasawa modules of ideal class groups on the one side and fine Selmer groups of abelian varieties on the other side. If $K_\infty$ contains…

The purpose of this paper is to propose a version of the notion of convenient Lie groupoid as a generalization of this concept in finite dimension. The authors point out which obstructions appear in the infinite dimensional context and how…

We construct certain absolutely irreducible Banach representations of the quaternion algebra of large canonical (Gelfand-Kirillov) dimension which yield counterexamples to a natural conjecture of Dospinescu-Schraen on the existence of an…

We formulate integral Iwasawa main conjectures for suitable twists of a newform $f$ that is non-ordinary at $p$, over the cyclotomic $\mathbb{Z}_p$-extension, the anticyclotomic $\mathbb{Z}_p$-extensions (in both the definite and the…

We introduce a new ideal {\mathfrak D} of the p-adic Galois group-ring associated to a real abelian field and a related ideal {\mathfrak J} for imaginary abelian fields. Both result from an equivariant, Kummer-type pairing applied to Stark…

A super Lie group is a group whose operations are $G^{\infty}$ mappings in the sense of Rogers. Thus the underlying supermanifold possesses an atlas whose transition functions are $G^{\infty}$ functions. Moreover the images of our charts…

We construct explicit proper p-harmonic functions on rank-one Lie groups of Iwasawa type. This class of Lie groups includes many classical Riemannian manifolds such as the rank-one symmetric spaces of non-compact type, Damek-Ricci spaces,…

For a large class of separable Banach spaces, we prove the real analytic Dolbeault Isomorphism Theorem for open subsets.

We give two integrability criteria for representations of Banach--Lie algebras as skew-symmetric unbounded operators on a dense domain of a Hilbert space.

We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically embeds. This solves a problem of J. Bourgain. We also give intrinsic characterizations of separable…

We construct a Banach Poisson-Lie group structure on the unitary group of a separable complex Hilbert space.

We prove that the classical integrability condition for almost complex structures on finite-dimensional smooth manifolds also works in infinite dimensions in the case of almost complex structures that are real analytic on real analytic…

Let $A$ be a Banach algebra and $I$ a dense ideal in $A$. A natural question in the theory of operator algebras is whether the property that all derivations $D: A \to I$ are inner (implemented by elements in $I$) implies that all…

Fix an odd prime $p$. Let $G$ be a compact $p$-adic Lie group containing a closed, normal, pro-$p$ subgroup $H$ which is abelian and such that $G/H$ is isomorphic to the additive group of $p$-adic integers $\mathbbZ_p$ . First we assume…

In this paper we explore the method of holomorphic induction for unitary representations of Banach--Lie groups. First we show that the classification of complex bundle structures on homogeneous Banach bundles over complex homogeneous spaces…