Counterexample to a question on the operator equation \(T(H^{1/n}T)^ n=K\)

DOI10.1016/0024-3795(92)90323-3zbMath0783.47021OpenAlexW1989515977WikidataQ125054855 ScholiaQ125054855MaRDI QIDQ1208270

Edward Bach, Takayuki Furuta

Publication date: 16 May 1993

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

Full work available at URL: https://doi.org/10.1016/0024-3795(92)90323-3

zbMATH Keywords

operator equationpositive operators on a Hilbert space

Mathematics Subject Classification ID

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

Related Items (3)

On the solution of nonlinear operator equations and the invariant subspace ⋮ 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

Cites Work

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