A NOTE ON QUADRATIC MAPS FOR HILBERT SPACE OPERATORS

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MORADI H.R.; ERFANIAN OMIDVAR M.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2017 | Volume:3 | Issue:10 Page(s): 31-36

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Title

A NOTE ON QUADRATIC MAPS FOR HILBERT SPACE OPERATORS

Author(s)

MORADI H.R. | ERFANIAN OMIDVAR M. | Issue Writer Certificate

Keywords

POSITIVE LINEAR MAPQ1

SESQUILINEAR MAPQ1

QUADRATIC MAPQ1

OPERATOR INEQUALITYQ1

Abstract

In this paper, we introduce the notion of SESQUILINEAR MAP on B (H). Based on this notion, we define the QUADRATIC MAP, which is the generalization of POSITIVE LINEAR MAP. With the help of this concept, we prove several well-known equality and inequality. In particular, we prove that if F is a quadratice map, A, B ∈ B (H) and p, q > 1 with 1/p + 1/q = 1, p ≤ q, then F(A - B) + F(1−p) A− B) ≤ pF(A) + qF(B).

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APA: Copy

MORADI, H.R., & ERFANIAN OMIDVAR, M.. (2017). A NOTE ON QUADRATIC MAPS FOR HILBERT SPACE OPERATORS. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 3(10), 31-36. SID. https://sid.ir/paper/257308/en

Vancouver: Copy

MORADI H.R., ERFANIAN OMIDVAR M.. A NOTE ON QUADRATIC MAPS FOR HILBERT SPACE OPERATORS. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2017;3(10):31-36. Available from: https://sid.ir/paper/257308/en

IEEE: Copy

H.R. MORADI, and M. ERFANIAN OMIDVAR, “A NOTE ON QUADRATIC MAPS FOR HILBERT SPACE OPERATORS,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 3, no. 10, pp. 31–36, 2017, [Online]. Available: https://sid.ir/paper/257308/en

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