Arithmetic Progressions and Its Applications to (m, q)-Isometries: A Survey

Bermúdez, Teresa; Martinón, Antonio; Noda, Juan Agust ́ õn

doi:10.1007/s00025-015-0470-2

Cited by 5 publications

(4 citation statements)

References 20 publications

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“…An arithmetic progression of order h is of strict order h if h = 0 or if h ≥ 1 and it is not of order h − 1. We refer the interested reader to [6] for complete details. Let a = (a j ) j≥0 be a numerical sequence.…”

Section: Example 33mentioning

confidence: 99%

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Some results on higher orders quasi-isometries

Mahmoud

Saddi

Gherairi

2020

Hacettepe Journal of Mathematics and Statistics

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The purpose of the present paper is to pursue further study of a class of linear bounded operators, known as n-quasi-m-isometric operators acting on an infinite complex separable Hilbert space H. We give an equivalent condition for any T to be n-quasi-m-isometric operator. Using this result we prove that any power of an n-quasi-m-isometric operator is also an n-quasi-m-isometric operator. In general the converse is not true. However, we prove that if T r and T r+1 are n-quasi-m-isometries for a positive integer r, then T is an n-quasi-m-isometric operator. We study the sum of an n-quasi-m-isometric operator with a nilpotent operator. We also study the product and tensor product of two n-quasi-misometries. Further, we define n-quasi strict m-isometric operators and prove their basic properties. Mathematics Subject Classification (2010). Primary 47B99; Secondary 47A05.Keywords. m-isometry, strict m-isometry, n-quasi-m-isometry.

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Section: Example 33mentioning

confidence: 99%

“…and it is not of order h − 1. We refer the interested reader to [5] for complete details. ).…”

mentioning

confidence: 99%

Some results on higher orders quasi-isometries

Mahmoud

Saddi

Gherairi

2020

Hacettepe Journal of Mathematics and Statistics

View full text Add to dashboard Cite

show abstract

“…We need some preliminaries about arithmetic progressions and their applications to -isometries. In [11], some results about this topic are recollected. Let be a commutative group and denote its operation by +.…”

Section: Preliminaries: Arithmetic Progressions and ( )-Isometriesmentioning

confidence: 99%

“…Conversely, if ( * ) ≥0 is an arithmetic progression of strict order − 1, then (10) and (11) hold. Taking = 0 we obtain (3), so is a strict -isometry.…”

Section: Theorem 1 Let Be a Hilbert Space An Operator ∈ ( ) Is A Stmentioning

confidence: 99%