1995
DOI: 10.1006/jmaa.1995.1188
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Polynomials on Banach Spaces: Zeros and Maximal Points

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Cited by 2 publications
(3 citation statements)
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“…Notice that, as an application of Lemma 3.2, the result obtained in Theorem 2.3 admits of an equivalent formulation in terms of capacities, namely, r ~(a + ~Bx) -1 + Ilal]" 4 …”
Section: D>_l Z6bx D>_lmentioning
confidence: 97%
See 1 more Smart Citation
“…Notice that, as an application of Lemma 3.2, the result obtained in Theorem 2.3 admits of an equivalent formulation in terms of capacities, namely, r ~(a + ~Bx) -1 + Ilal]" 4 …”
Section: D>_l Z6bx D>_lmentioning
confidence: 97%
“…The proof of Theorem 2.1 relies on an infinite-dimensional version of Bernstein's inequality due to Harris [3], who stated it only for homogeneous polynomials, although it also works for arbitrary polynomials, as Tonge and Lacruz [4] pointed out. Notice that these definitions also make sense when S is a subset of a complex Banach space X.…”
Section: Theorem 21 Let X Be a Complex Banach Space Let D > 1 And mentioning
confidence: 99%
“…In recent years there has been considerable interest in the study of geometric properties of the space P( k E). It has been shown not to be strictly convex [13], extremal and smooth points of the unit ball have been characterised for a number of spaces ( [3], [4], [5], [6], [7], [8], [9], [10]), and related problems have been considered, often in the finite-dimensional setting ( [1], [2], [11], [12]).…”
mentioning
confidence: 99%