Common zeros preserving maps on vector-valued function spaces and Banach modules

Hosseini, Maliheh; Sady, Fereshteh

doi:10.5565/publmat_60216_10

Cited by 2 publications

(3 citation statements)

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“…, X n of X . The next theorem gives a module version of a known result concerning common zero-preserving maps for certain subspaces of vector-valued continuous functions (see [9], [12], and [19]). Before stating the theorem we introduce the notion of Z-regularity of Banach modules.…”

Section: Proof Consider the Natural Map νmentioning

confidence: 97%

“…Since common zero-preserving maps between subspaces of continuous vector-valued functions may be compared with maps preserving joint spectrums in a commutative unital Banach algebra case, then the results concerning such maps can also be considered as generalizations of the Gleason-Kakane-Żelazko theorem. For some recent results on this topic, see [9], [12], and [19].…”

Section: Introductionmentioning

confidence: 99%

“…Proof. The proof is a modification of Theorem 4.5 in [12]. For each ϕ ∈ Θ(X ), we set I ϕ := ϕ∈Z(x) Z(T x) ∩ Θ(Y).…”

mentioning

confidence: 99%

See 2 more Smart Citations

Point multipliers and the Gleason–Kahane–Żelazko theorem

Ghodrat¹,

Sady²

2017

Banach J. Math. Anal.

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Let A be a Banach algebra, and let X be a left Banach A-module. In this paper, using the notation of point multipliers on left Banach modules, we introduce a certain type of spectrum for the elements of X and we also introduce a certain subset of X which behaves as the set of invertible elements of a commutative unital Banach algebra. Among other things, we use these sets to give some Gleason-Kahane-Żelazko theorems for left Banach A-modules.

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Section: Proof Consider the Natural Map νmentioning

confidence: 97%