Automatic Boundedness of Adjointable Operators on Barreled VH-Spaces

2021/07/30 by Serdar Ay, Ay, Serdar · 1 citation
Mathematics · #Advanced Operator Algebra Research #Holomorphic and Operator Theory #Advanced Banach Space Theory

paper · pdf · doi:10.1007/s11785-021-01184-6

Abstract

We consider the space of adjointable operators on barreled VH (Vector Hilbert) spaces and show that such operators are automatically bounded.This generalizes the well known corresponding result for locally Hilbert C^*-modules.We pick a consequence of this result in the dilation theory of VH-spaces and show that, when barreled VH-spaces are considered, a certain boundedness condition for the existence of VH-space linearisations, equivalently, of reproducing kernel VH-spaces, is automatically satisfied.

Cited by

• Isometric representations of calibrated ordered spaces on C(X)

Related

• Locally adjointable operators on Hilbert C^*-modules
• Representations of *-semigroups associated to invariant kernels with values continuously adjointable operators
• Adjoint for Operators in Banach Spaces
• Operator Models for Hilbert Locally C^*-Modules
• A new uniform structure for Hilbert C^*-modules