International Journal of Science and Research (IJSR)

International Journal of Science and Research (IJSR)
Call for Papers | Open Access | Double Blind Reviewed

ISSN: 2319-7064


Downloads: 3

Research Paper | Mathematics | Kenya | Volume 10 Issue 11, November 2021


Quasiaffine Inverses of Linear Operators in Hilbert Spaces

J. M. Mwanzia | M. Kavila | J. M. Khalagai


Abstract: Abstract: Let H denote a complex Hilbert space and B (H) denote the Banach algebra of bounded linear operators on H. Given operators A, B, X ∈ B (H), we define R (A, B) : B (H) → B (H) by R (A, B) X = AXB - X and C (A, B) : B (H) → B (H) by C (A, B) X = AX - XB. In this paper, we investigate properties of the operators A, B ∈ B (H) satisfying R (A, B) X = 0 or R (B, A) Y = 0 or both where X and Y are one-one or have a dense range or both. In particular, the case R (A, B) X = 0 = R (B, A) Y is of special interest with respect to invertibility of the operator A under some classes of operators.


Keywords: quasiaffinity, quasiaffine inverse and invertibility of operators


Edition: Volume 10 Issue 11, November 2021,


Pages: 1076 - 1082


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How to Cite this Article?

J. M. Mwanzia, M. Kavila, J. M. Khalagai, "Quasiaffine Inverses of Linear Operators in Hilbert Spaces", International Journal of Science and Research (IJSR), Volume 10 Issue 11, November 2021, pp. 1076-1082, https://www.ijsr.net/get_abstract.php?paper_id=SR211116150836

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