Nonlinear maps commuting with the [lambda]-Aluthge transform under (n,m)-Jordan-triple product

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Nonlinear maps commuting with the [lambda]-Aluthge transform under (n,m)-Jordan-triple product

Chabbabi, Fadil; Mbekhta, Mostafa

Linear & multilinear algebra, 12/2019, Volume: 67, Issue: 12

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In this paper, we give a complete form of bijective (not necessarily linear) maps Formula omitted. where H,K are Hilbert spaces with Formula omitted. that satisfy Formula omitted. where Formula omitted. is the λ-Aluthge transform of T and the operation Formula omitted. is the Formula omitted. -Jordan-triple product. We show that there exists a unitary or anti-unitary operator Formula omitted. and a constant Formula omitted. , with Formula omitted. such that Formula omitted.

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