Automatic Boundedness of Adjointable Operators on Barreled VH-Spaces

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2022

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Springer Basel Ag

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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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.

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Ordered *-space, Admissible space, VH-space, Barreled VH-space, Adjointable operators, Bounded operators, Positive semidefinite kernel, Invariant kernel, Linearisation, Reproducing kernel, *-Representation, Locally C*-algebra, Hilbert locally C*-module

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16

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1

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https://doi.org/10.1007/s11785-021-01184-6
 https://hdl.handle.net/20.500.14411/1642

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