The operator equation \(T(H^{1/n}T)^ n=K\)

DOI10.1016/0024-3795(88)90205-4zbMath0664.47011OpenAlexW2075380177MaRDI QIDQ1114913

Takayuki Furuta

Publication date: 1988

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(88)90205-4

zbMATH Keywords

positive solutionnonsingularbounded positive operators on a Hilbert space

Mathematics Subject Classification ID

Equations involving linear operators, with operator unknowns (47A62)

Related Items (6)

On operator order and chaotic operator order for two operators ⋮ On the solution of nonlinear operator equations and the invariant subspace ⋮ Pedersen-Takesaki operator equation and operator equation \(AX = B\) in Hilbert \(C^*\)-modules ⋮ The Furuta inequality and an operator equation for linear operators ⋮ The operator equation \(K^p = H^{\frac \delta 2}T^{\frac 1 2}(T^{\frac 1 2}H^{\delta +r}T^{\frac 1 2})^{\frac {p-\delta}{\delta +r}}T^{\frac 1 2}H^{\frac \delta 2}\) and its applications ⋮ Counterexample to a question on the operator equation \(T(H^{1/n}T)^ n=K\)

Cites Work

• Unnamed Item
• On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space
• Shorter Notes: The Operator Equation THT = K
• $A \geq B \geq 0$ Assures $(B^r A^p B^r)^{1/q} \geq B^{(p+2r)/q$ for $r \geq 0$, $p \geq 0$, $q \geq 1$ with $(1 + 2r)q \geq p + 2r$

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