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Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars $\mathbb{R}$ or $\mathbb{C}$ by a real or complex Dedekind complete unital…

An operator C on a Hilbert space H dilates to an operator T on a Hilbert space K if there is an isometry V from H to K such that C=V^*TV. A main result of this paper is, for a positive integer d, the simultaneous dilation, up to a sharp…

Functional Analysis · Mathematics 2019-06-05 J. William Helton , Igor Klep , Scott A. McCullough , Markus Schweighofer

Let $\mathcal{B} (X)$ be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space $X$. In this note, we show that a lemma used in the proof of the main result of [ Taghavi and Hosseinzadeh, linear and…

Functional Analysis · Mathematics 2024-12-03 S. Elouazzani , M. Elhodaibi , S. Saber

We construct a weak dilation of a not necessarily unital CP-semigroup to an E-semigroup acting on the adjointable operators of a Hilbert module with a unit vector. We construct the dilation in such a way that the dilating E-semigroup has a…

Operator Algebras · Mathematics 2013-11-20 Michael Skeide

In the literature surrounding the theory of Banach spaces, considerable effort has been invested in exploring the conditions on a Banach space X that characterise X as being an inner product space or as a linearly isomorphic copy of a…

Functional Analysis · Mathematics 2024-12-31 M. A. Sofi

A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…

General Relativity and Quantum Cosmology · Physics 2010-11-01 Jorma Louko

We introduce a natural notion of holomorphic map between generalized complex manifolds and we prove some related results on Dirac structures and generalized Kaehler manifolds.

Differential Geometry · Mathematics 2015-05-13 Liviu Ornea , Radu Pantilie

We study hermitian operators and isometries on spaces of vector-valued Lipschitz maps with the sum norm: $\|\cdot\|_{\infty}+L(\cdot)$. There are two main theorems in this paper. Firstly, we prove that every hermitian operator on…

Functional Analysis · Mathematics 2024-11-20 Shiho Oi

We present a set-theoretic version of some basic dilation results of operator theory. The results we have considered are Wold decomposition, Halmos dilation, Sz. Nagy dilation, inter-twining lifting, commuting and non-commuting dilations,…

Operator Algebras · Mathematics 2020-04-21 B V Rajarama Bhat , Sandipan De , Narayan Rakshit

We investigate the invariance properties of general wavelet coorbit spaces and Besov-type decomposition spaces under dilations by matrices. We show that these matrices can be characterized by quasi-isometry properties with respect to a…

Functional Analysis · Mathematics 2023-04-03 Hartmut Führ , Reihaneh Raisi Tousi

In this paper we study commuting families of holomorphic mappings in $\mathbb{C}^n$ which form abelian semigroups with respect to their real parameter. Linearization models for holomorphic mappings are been used in the spirit of…

Complex Variables · Mathematics 2008-12-25 Filippo Bracci , Mark Elin , David Shoikhet

We provide sufficient conditions for a mapping between two Banach spaces to be a diffeomorphism using the approach of an auxiliary functional and also by the aid of a duality mapping corresponding to a normalization function. We simplify…

Functional Analysis · Mathematics 2018-09-17 Marek Galewski , Dušan Repovš

We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. The main difficulty is to find a suitable notion of algebra homotopy that generalizes to algebras over operads O. To solve this…

Algebraic Topology · Mathematics 2016-01-20 Alexander Berglund

This paper considers dilations and translations of lines in the Desargues affine plane. A dilation of a line transforms each line into a parallel line whose length is a multiple of the length of the original line. In addition to the usual…

Metric Geometry · Mathematics 2021-07-23 Orgest Zaka , James F. Peters

The duality of uniform approximation property for Banach spaces is well known. In this note, we establish, under the assumption of local reflexivity, the duality of uniform approximation property in the category of operator spaces.

Operator Algebras · Mathematics 2014-10-28 Yanqi Qiu

We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…

Algebraic Geometry · Mathematics 2010-03-31 Tristram de Piro

A previous article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs. They have infinite-dimensional Lie point symmetry groups…

Mathematical Physics · Physics 2018-05-09 Vladimir A. Dorodnitsyn , Roman Kozlov , Sergey V. Meleshko , Pavel Winternitz

The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the…

Operator Algebras · Mathematics 2007-05-23 David P. Blecher , Edward G. Effros , Vrej Zarikian

This paper studies the diameter of the numerical range of bounded operators on Hilbert space and the induced seminorm, called the numerical diameter, on bounded linear maps between operator systems which is sensible in the case of unital…

Functional Analysis · Mathematics 2024-07-03 Niel de Beaudrap , Christopher Ramsey

We generalize several important results from the perturbation theory of linear operators to the setting of semisimple orthogonal symmetric Lie algebras. These Lie algebras provide a unifying framework for various notions of matrix…

Representation Theory · Mathematics 2023-07-04 Emanuel Malvetti , Gunther Dirr , Frederik vom Ende , Thomas Schulte-Herbrüggen