\(T^*T\) always has a positive selfadjoint extension

DOI10.1007/s10474-011-0154-7zbMath1258.47015OpenAlexW2036612628MaRDI QIDQ1928060

Zs. Tarcsay, Zoltán Sebestyén

Publication date: 2 January 2013

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-011-0154-7

zbMATH Keywords

operator extensionselfadjoint operatorpositive operatorFriedrichs extensionKrein-von Neumann extensionclosable operator

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) Dilations, extensions, compressions of linear operators (47A20)

Related Items (16)

Extremal maximal sectorial extensions of sectorial relations ⋮ Von Neumann’s theorem for linear relations ⋮ Certain properties involving the unbounded operators \(p(T)\), \(TT^\ast\), and \(T^\ast T\); and some applications to powers and \textit{nth} roots of unbounded operators ⋮ Unbounded operators having self‐adjoint, subnormal, or hyponormal powers ⋮ Reduction of positive self-adjoint extensions ⋮ A generalized von Neumann's theorem for linear relations in Hilbert spaces ⋮ On the adjoint of Hilbert space operators ⋮ Closed range positive operators on Banach spaces ⋮ On form sums of positive operators ⋮ A Class of Sectorial Relations and the Associated Closed Forms ⋮ Self-adjointness and skew-adjointness criteria involving powers of linear relations ⋮ Adjoint to each other linear relations. Nieminen type criteria ⋮ Essentially self-adjoint linear relations in Hilbert spaces ⋮ On the adjoint of linear relations in Hilbert spaces ⋮ Factorized sectorial relations, their maximal-sectorial extensions, and form sums ⋮ A matrix formula for Schur complements of nonnegative selfadjoint linear relations

Cites Work

• Operational calculus of linear relations
• On suboperators with codimension one domains
• On a singular part of an unbounded operator
• Über adjungierte Funktionaloperatoren
• Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren. I
• On products of unbounded operators
• Positive selfadjoint extensions of positive symmetric operators
• On characteristic properties of singular operators
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