Geodesic
Higher dimensional [m, C]-isometric commuting d-tuple of operators
Filomat, Tome 36 (2022) no. 12, p. 4173

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DOI

In this paper we recover an [m,C]-isometric operators and (m, C)-isometric commuting tuples of operators on a Hilbert space studied respectively in [11] and [16], we introduce the class of [m,C]-isometries for tuple of commuting operators. This is a generalization of the class of [m,C]-isometric commuting operators on a Hilbert spaces. A commuting tuples of operators S = (S1, · · · ,Sp) ∈ B(H)p is said to be [m,C]-isometric p-tuple of commuting operators if Ψm ( S,C ) := m∑ j=0 (−1)m− j ( m j )(∑ |α|= j j! α! CSαCSα ) = 0 for some positive integer m and some conjugation C. We consider a multi-variable generalization of these single variable [m,C]-isometric operators and explore some of their basic properties.
DOI : 10.2298/FIL2212173A
Classification : 47B20, 47B99
Keywords: [m, C]-isometric operators, (m, C)-isometric commuting tuple of operator, Hilbert space 
Ahmed Himadan Ahmed. Higher dimensional [m, C]-isometric commuting d-tuple of operators. Filomat, Tome 36 (2022) no. 12, p. 4173 . doi: 10.2298/FIL2212173A
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     author = {Ahmed Himadan Ahmed},
     title = {Higher dimensional [m, {C]-isometric} commuting d-tuple of operators},
     journal = {Filomat},
     pages = {4173 },
     year = {2022},
     volume = {36},
     number = {12},
     doi = {10.2298/FIL2212173A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2212173A/}
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