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ReserarchID
NUDJ9
Crossref Journal DOI 10.17406/GJSFR
Print ISSN 0975-5896
e-ISSN 2249-4626
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In this paper, apply an established transference principle to obtain the boundedness of certain functional calculi for the sequence of semigroup generators. It is proved thatif -𝐴𝐴 𝑗𝑗 be the sequence generates 𝐶𝐶 0 -semigroups on a Hilbert space, then for each 𝜀𝜀 > -1 the sequence of operators 𝐴𝐴 𝑗𝑗 has bounded calculus for the closed ideal of bounded holomorphic functions on right half-plane. The bounded of this calculus grows at most logarithmically as(1 + 𝜀𝜀) ↘ 0. As a consequence decay at ∞. Then showed that each sequence of semigroup generator has a socalled (strong) m-bounded calculus for all m ∈ ℕ, and that this property characterizes the sequence of semigroup generators. Similar results are obtained if the underlying Banach space is a UMD space. Upon restriction to so-called 𝛾𝛾 𝑗𝑗 -𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 semigroups, the Hilbert space results actually hold in general Banach spaces.
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