Hilbert–Schmidt operator
id:
hilbert-schmidt-operator-190-1013316
title:
Hilbert–Schmidt operator
text:
In mathematics, a Hilbert–Schmidt operator, named after David Hilbert and Erhard Schmidt, is a bounded operator A : H → H that acts on a Hilbert space H and has finite Hilbert–Schmidt norm ‖ A ‖ HS 2 = def ∑ i ∈ I ‖ A e i ‖ H 2, where { e i : i ∈ I } is an orthonormal basis. The index set I need not be countable. However, the sum on the right must contain at most countably many non-zero terms, to have meaning. This definition is independent of the choice of the orthonormal basis. In finite-d
brand slug:
wiki
category slug:
encyclopedia
description:
Topic in mathematics
original url:
https://en.wikipedia.org/wiki/Hilbert%E2%80%93Schmidt_operator
date created:
2004-09-11T15:08:02Z
date modified:
2024-09-09T12:39:58Z
main entity:
{"identifier":"Q1518047","url":"https://www.wikidata.org/entity/Q1518047"}
image:
fields total:
13
integrity:
15