Geodesic
(m,∞)-expansive and (m,∞)-contractive commuting tuple of operators on a Banach space
Filomat, Tome 36 (2022) no. 4, p. 1113

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For a d-tuple of commuting operators S := (S 1 , · · · , S d) ∈ B[X] d , m ∈ N and p ∈ (0, ∞), we define Q (p) m (S; u) := 0≤k≤m (−1) k m k µ ∈ N d 0 |µ| = k k! µ S µ u p. As a natural extension of the concepts of (m, p)-expansive and (m, p)-contractive for tuple of commuting operators, we introduce and study the concepts of (m, ∞)-expansive tuple and (m, ∞)-contractive tuple of commuting operators acting on a Banach space. We say that S is (m, ∞)-expansive d-tuple resp. (m, ∞)-contractive d-tuple of operators if Q (p) m (S; u) ≤ 0 ∀ u ∈ X and p → ∞ resp. Q (p) m (S; u) ≥ 0 ∀ u ∈ X and p → ∞. These concepts extend the definition of (m, ∞)-isometric tuple of bounded linear operators acting on Banach spaces was introduced and studied in [13].
DOI : 10.2298/FIL2204113A
Classification : 47A05, 47A10, 47A11
Keywords: m-isometric tuple, (m, p)-isometric tuples, expansive operator, contractive operator 
Hadi Obaid Alshammari; Sid Ahmed Ould Ahmed Mahmoud. (m,∞)-expansive and (m,∞)-contractive commuting tuple of operators on a Banach space. Filomat, Tome 36 (2022) no. 4, p. 1113 . doi: 10.2298/FIL2204113A
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     title = {(m,\ensuremath{\infty})-expansive and (m,\ensuremath{\infty})-contractive commuting tuple of operators on a {Banach} space},
     journal = {Filomat},
     pages = {1113 },
     year = {2022},
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     doi = {10.2298/FIL2204113A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2204113A/}
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