Related papers: Hadamard's lemma in separable Hilbert spaces

We generalize P. M. Neumann's Lemma to the setting of isometric actions on metric spaces and use it to prove several results in continuous logic related to algebraic independence. In particular, we show that algebraic independence satisfies…

This paper uses differential spaces to obtain some new results in integrable Hamiltonian systems

We extend the definition of an extension of a right Hilbert module to the setting of Hilbert bimodules and show that an extension of Hilbert bimodules induces an extension of Cuntz-Pimsner algebras. We also study the Cuntz-Pimsner algebra…

We study scattered piecewise interpretable Hilbert spaces from a model theoretic point of view. We establish strong connections between the Hilbert space structure theorems of [Chevalier Hrushovski 2021] and the model theoretic notions of…

This paper presents a bicomplex version of the Spectral Decomposition Theorem on infinite dimensional bicomplex Hilbert spaces. In the process, the ideas of bounded linear operators, orthogonal complements and compact operators on bicomplex…

In this paper, the notions of first-order and second-order generalized linear spans and index set are defined. Moreover, their properties are investigated and applied to the studies of extension of isometries. We develop the theory of…

In this paper, we propose the study of a conjecture whose affirmative solution would provide an example of a non-convex Chebyshev set in an infinite-dimensional real Hilbert space.

The converse of Fortin's Lemma in Banach spaces is established in this Note.

We study some examples when there is actually an equality in the linear algebra bound. When the vectors considered span in fact the entire space. We would like to point out that in some cases this provides some interesting extra information…

The notion of prolongation of an algebraic variety is developed in an abstract setting that generalises the difference and (Hasse) differential contexts. An interpolating map that compares the prolongation spaces with algebraic jet spaces…

We propose global surjectivity theorems of differentiable maps based on second order conditions. Using the homotopy continuation method, we demonstrate that, for a $C^2$ differentiable map from a Hilbert space to a finite-dimensional…

We will formulate and prove a generalization of the isoperimetric inequality in the plane. Using this inequality we will construct an unitary space - and in consequence - an isomorphic copy of a separable infinite dimensional Hilbert space,…

We study the relative position of three subspaces in a separable infinite-dimensional Hilbert space. In the finite-dimensional case, Brenner described the general position of three subspaces completely. We extend it to a certain class of…

In the context of extriangulated categories, we establish the injective version of Schanuel's lemma in homological algebra.

In [{\it On the free implicative semilattice extension of a Hilbert algebra}. Mathematical Logic Quarterly 58, 3 (2012), 188--207], Celani and Jansana give an explicit description of the free implicative semilattice extension of a Hilbert…

We study a cut-off function lemma in projective spaces. We believe that this is well-known. We provide the details of the computation for later uses.

We prove a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces.

$\lambda$-Scale is an enrichment of lambda calculus which is adapted to emergent algebras. It can be used therefore in metric spaces with dilations.

In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.

The completeness of Gaussians in a Hilbert functional space is established