본문 바로가기
KERD
논문KCI 등재

The Polynomial Numerical Index of Lp(μ)

김성권
경북대학교 자연과학대학 수학과|2013.03|Kyungpook Mathematical Journal|제53권 제1호|pp. 117-124

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

polynomial numerical indexHomogeneous polynomials
주제분류수학

초록

We show that for 1 < p < ∞, k,m ∈ N, n(k)(lp) = inf{n(k)(lm p ) : m ∈ N}and that for any positive measure μ, n(k)(Lp(μ)) ≥ n(k)(lp). We also prove that for every Q ∈ P(klp : lp) (1 < p < ∞), if v(Q) = 0, then ∥Q∥ = 0.

Abstract

We show that for 1 < p < ∞, k,m ∈ N, n(k)(lp) = inf{n(k)(lm p ) : m ∈ N}and that for any positive measure μ, n(k)(Lp(μ)) ≥ n(k)(lp). We also prove that for every Q ∈ P(klp : lp) (1 < p < ∞), if v(Q) = 0, then ∥Q∥ = 0.

참고문헌 (12)

  1. F. F. Bonsall, "Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras" (1971), Cambridge Univ. Press
  2. F. F. Bonsall, "Numerical Ranges II" (1973), Cambridge Univ. Press
  3. Y. S. Choi, "Norm or numerical radius attaining multilinear mappings and polynomials", J. London Math. Soc, 54, pp.135~147 (1996)
  4. Y. S. Choi, "The polynomial numerical index of a Banach space", Proc. Edinburgh Math. Soc., 49, pp.39~52 (2006)
  5. Y. S. Choi, "Composition, numerical range and Aron-Berner extension", Math. Scand., 103, pp.97~110 (2008)
  6. S. Dineen, "Complex Analysis on In nite Dimensional Spaces" (1999), Springer-Verlag
  7. J. Duncan, "The numerical index of a normed space", J. London Math. Soc., 2, pp.481~488 (1970)
  8. Sung Guen Kim, "Norm and Numerical Radius of 2-homogeneous Polynomials on the Real Space l^{2}_{p}, (1 < p < infinite)", Kyungpook Mathematical Journal, 48(3), pp.387~393 (2008), 경북대학교 자연과학대학 수학과
  9. S. G. Kim, "Three kinds of numerical indices of a Banach space", Math. Proc. Royal Irish Acad., 112A, pp.21~35 (2012)
  10. S. G. Kim, "On the polynomial numerical index of the real spaces c0, ℓ1, ℓ1", J. Math. Anal. Appl., 337, pp.98~106 (2008)
  11. H. J. Lee, "Banach spaces with polynomial numerical index 1", Bull. Lond. Math. Soc., 40, pp.193~198 (2008)
  12. G. Lumer, "Semi-inner-product spaces", Trans. Amer. Math. Soc., 100, pp.29~43 (1961)

관련 논문AI추천

Polynomial Numerical Index of lp (1 < p < 1)김성권경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제3호Some observations on the numerical index and the polynomial numerical indexSun Kwang Kim대한수학회 · 대한수학회보2016 · 제53권 제1호Polynomial factorization through L_r(μ) spacesJoaquin M. Gutierrez, Raffaella Cilia대한수학회 · 대한수학회지2009 · 제46권 제6호Norm and Numerical Radius of 2-homogeneous Polynomials on the Real Space l^{2}_{p}, (1 < p < infinite)Sung Guen Kim경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2008 · 제48권 제3호The ideal of weakly $p$-nuclear operators and its injective and surjective hulls김주명대한수학회 · 대한수학회지2019 · 제56권 제1호Characterization of operators taking P-summable sequences into sequences in the range of a vector measure송희자영남수학회 · East Asian Mathematical Journal2008 · 제24권 제2호

이 간행물의 다른 논문 (11건)

Subordination and Superordination for Multivalent Functions associated with the Differintegral Operator조낙은, 권오상pp. 1-12Fekete-Szego Problem for a Generalized Subclass of Analytic FunctionsMurat Caglar, Halit Orhan, Nihat Yagmurpp. 13-23Module-theoretic Characterizations of Strongly t-linked Ex- tensions권태인, 김환구pp. 25-35Characterizations of Several Modules Relative to the Class of B(M, X)Yahya Talebi, Mehrab Hosseinpourpp. 37-47A Note on Maass-Jacobi Forms II양재현pp. 49-86
원문 보기