An isometry plus a nilpotent operator is an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>m</mml:mi></mml:math>-isometry. Applications

Bermúdez, Teresa; Martinón, Antonio; Noda, Juan Agustín

doi:10.1016/j.jmaa.2013.05.043

Cited by 44 publications

(29 citation statements)

References 23 publications

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“…This result of [11] in turn provides the affirmative answer to a conjecture in F. Botelho and J. Jamison [10]. Recently the notion of m-isometry has been generalized to Banach space operators and the more general version in Banach spaces has been obtained in [9] by T. Bermúdez, A. Martinón and J. Noda.…”

Section: Remark 8 Let a B ∈ L(h)supporting

confidence: 54%

“…This is a main theorem of the paper[8] by T. Bermúdez, A. Martinón and J. Noda.The following computation shows that when m > 1, Q * −1 β m−1 (A)Q −1 could equal zero. Let A 1 be a strict m-isometry and Q 1 is a nilpotent operator of order .…”

mentioning

confidence: 75%

“…The case when A is self adjoint was studied by [7,12], and [13]. The case when A is an isometry was studied in [8].…”

Section: And T ∈ L(h) the Definition Of P(t ) In The Hereditary Funcmentioning

confidence: 99%

“…The paper [8] proves that V + Q is a strict (2n − 1)-isometry if V is an isometry, Q is a nilpotent operator with order n, and V commutes with Q, but does not consider the case when V is an m-isometry with m > 1. Theorem 4 generalizes this result to the sum of an m-isometry and a nilpotent operator.…”

Section: Sum With a Nilpotent Operatormentioning

confidence: 99%

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Some results on higher order isometries and symmetries: Products and sums with a nilpotent operator

Gu¹,

Stankus²

2015

Linear Algebra and its Applications

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MSC: 47A62 47A05 47B99 Keywords: Hilbert Space m-Isometric operator n-Symmetric operator Elementary operators Nilpotent operators Tensor products Linear transformationsWe study the sum of an m-isometry or an m-symmetric operator with a nilpotent operator. We also study the product of two m-isometries or two n-symmetries. We obtain several theorems generalizing previous work. Our method is straightforward and thus offers direct and simple insights into why these theorems are true.We will use the hereditary functional calculus which was developed by J. Agler [1] and motivated by the work of W.J. Helton and J. Ball [12,7]. Let H be a Hilbert space and L(H) be the set of all bounded linear operators on H. For a polynomial p(x, y) in two variables x and y, p(x, y) = m k=0 m =0 c k y x k , c k ∈ C

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Section: Remark 8 Let a B ∈ L(h)supporting

confidence: 54%

mentioning

confidence: 75%

“…The case when A is self adjoint was studied by [7,12], and [13]. The case when A is an isometry was studied in [8].…”

Section: And T ∈ L(h) the Definition Of P(t ) In The Hereditary Funcmentioning

confidence: 99%

Section: Sum With a Nilpotent Operatormentioning

confidence: 99%

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Some results on higher order isometries and symmetries: Products and sums with a nilpotent operator

Gu¹,

Stankus²

2015

Linear Algebra and its Applications

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“…The concept of left n-invertible operators is motivated by the m-isometries studied earlier in [2]- [6], [24] on Hilbert spaces and more recently in [9], [11]- [13], [15], [26] on Hilbert spaces and [7], [8], [10], [16], [22] on Banach spaces. An operator T on a Hilbert space is an n-isometry if β n (T * , T ) = 0, that is, T * is a left n-inverse of T.…”

mentioning

confidence: 99%

Structures of left n-invertible operators and their applications

2015

Studia Math.

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We study left n-invertible operators introduced in two recent papers. We show how to construct a left n-inverse as a sum of a left inverse and a nilpotent operator. We provide refinements for results on products and tensor products of left n-invertible operators by Duggal and Müller (2013). Our study leads to improvements and different and often more direct proofs of results of Duggal and Müller (2013) and Sid Ahmed (2012). We make a conjecture about tensor products of left n-invertible operators and prove this conjecture in several cases. Finally, applications of these results are given to left n-invertible elementary operators and essentially left n-invertible operators.

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Some Examples of m-Isometries

2020

Self Cite

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We obtain the admissible sets on the unit circle to be the spectrum of a strict m-isometry on an n-finite dimensional Hilbert space. This property gives a better picture of the correct spectrum of an m-isometry. We determine that the only m-isometries on R 2 are 3-isometries and isometries giving by ±I + Q, where Q is a nilpotent operator. Moreover, on real Hilbert space, we obtain that m-isometries preserve volumes. Also we present a way to construct a strict (m + 1)-isometry with an m-isometry given, using ideas of Aleman and Suciu [7, Proposition 5.2] on infinite dimensional Hilbert space.Date: February 25, 2019.2010 Mathematics Subject Classification. 47A05. Key words and phrases. m-isometry, strict m-isometry, weighted shift operator, isometric n-Jordan operator, sub-isometric n-Jordan operator, finite dimensional space, k-volume.

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An isometry plus a nilpotent operator is anm-isometry. Applications

Cited by 44 publications

References 23 publications

Some results on higher order isometries and symmetries: Products and sums with a nilpotent operator

Some results on higher order isometries and symmetries: Products and sums with a nilpotent operator

Structures of left n-invertible operators and their applications

Some Examples of m-Isometries

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