Holomorphic Automorphisms of the Unit Balls of Hilbert C $^*$ -Modules

Isidro, José M.

doi:10.1017/s0017089503001216

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2013

2024

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Cited by 6 publications

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“…In [5], J. M. Isidro shows that every Hilbert C * -module is a JB * -triple with the Jordan triple product {x, y, z} = 1 2 (x y, z + z y, x ).…”

Section: Preliminariesmentioning

confidence: 99%

Inner products and module maps of Hilbert C*-modules

Hsu,

Wong

2014

Preprint

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Let E and F be two Hilbert C * -modules over C * -algebras A and B, respectively. Let T be a surjective linear isometry from E onto F and ϕ a map from A into B. We will prove in this paper that if the C * -algebras A and B are commutative, then T preserves the inner products and T is a module map, i.e., there exists a * -isomorphism ϕ between the C * -algebras such that T x, T y = ϕ( x, y ), and T (xa) = T (x)ϕ(a). In case A or B is noncommutative C * -algebra, T may not satisfy the equations above in general. We will also give some condition such that T preserves the inner products and T is a module map.2000 Mathematics Subject Classification. 46L08, 46E40, 46B04. Key words and phrases. Hilbert C * -modules, TROs, complete isometries, triple products, Banach-Stone type theorems.This work is jointly supported by a Taiwan NSC Grant ().

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“…In [5], J. M. Isidro shows that every Hilbert C * -module is a JB * -triple with the Jordan triple product {x, y, z} = 1 2 (x y, z + z y, x ).…”

Section: Preliminariesmentioning

confidence: 99%

Inner products and module maps of Hilbert C*-modules

Hsu,

Wong

2014

Preprint

View full text Add to dashboard Cite

show abstract

“…(see [34,Theorem 1.4]). By a little abuse of notation, the symbol •|• will indistinctly stand for the inner product of H and the C(K)-valued inner product of C(K, H).…”

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confidence: 99%