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Volume 37, Issue 2
The Reflexive Selfadjoint Solutions to Some Operator Equations

Wenting Liang & Chunyuan Deng

DOI: 10.4208/cmr.2021-0006

Commun. Math. Res., 37 (2021), pp. 236-254.

Published online: 2021-04

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  • Abstract

In this paper, we study the existence of the reflexive, reflexive self-adjoint and reflexive positive solutions to some operator equations with respect to the generalized reflection operator dual $(P,Q)$. We derive necessary and sufficient conditions for the solvability of these equations and provide a detailed description of the solutions in the solvable case by using the Moore-Penrose inverses.

  • Keywords

$(P,Q)$ reflexive solution, operator equation, positive operator.

  • AMS Subject Headings

15A09, 47A05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-37-236, author = {Liang , Wenting and Deng , Chunyuan}, title = {The Reflexive Selfadjoint Solutions to Some Operator Equations}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {37}, number = {2}, pages = {236--254}, abstract = {

In this paper, we study the existence of the reflexive, reflexive self-adjoint and reflexive positive solutions to some operator equations with respect to the generalized reflection operator dual $(P,Q)$. We derive necessary and sufficient conditions for the solvability of these equations and provide a detailed description of the solutions in the solvable case by using the Moore-Penrose inverses.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0006}, url = {http://global-sci.org/intro/article_detail/cmr/18739.html} }
TY - JOUR T1 - The Reflexive Selfadjoint Solutions to Some Operator Equations AU - Liang , Wenting AU - Deng , Chunyuan JO - Communications in Mathematical Research VL - 2 SP - 236 EP - 254 PY - 2021 DA - 2021/04 SN - 37 DO - http://doi.org/10.4208/cmr.2021-0006 UR - https://global-sci.org/intro/article_detail/cmr/18739.html KW - $(P,Q)$ reflexive solution, operator equation, positive operator. AB -

In this paper, we study the existence of the reflexive, reflexive self-adjoint and reflexive positive solutions to some operator equations with respect to the generalized reflection operator dual $(P,Q)$. We derive necessary and sufficient conditions for the solvability of these equations and provide a detailed description of the solutions in the solvable case by using the Moore-Penrose inverses.

Liang , Wenting and Deng , Chunyuan. (2021). The Reflexive Selfadjoint Solutions to Some Operator Equations. Communications in Mathematical Research . 37 (2). 236-254. doi:10.4208/cmr.2021-0006
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