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Nilpotent perturbations of m-isometric and m-symmetric tensor products of commuting d-tuples of operators

Duggal Bhagwati Prashad, Kim Hyoun

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20230146

If T1 and T2 are commuting d -tuples of Hilbert space operators in B(H)d such that (T∗1⊗I+I⊗T∗2,T1⊗I+I⊗T2) is strictly m -isometric (resp., m -symmetric) for some positive integer m , then there exist a scalar d -tuple λ and positive integers mi , 1≤i≤2 , such that m=m1+2m2−2 , (T∗1+¯λ,T1+λ) is m1 isometric, and T2−λ is m2 -nilpotent (resp., m=m1+m2−1 , (T∗1+¯λ,T1+λ) is m1 -symmetric and (T∗2−¯λ,T2−λ) is m2 symmetric).