본문 바로가기
KERD
논문KCI 등재

Norm and Numerical Radius of 2-homogeneous Polynomials on the Real Space l^{2}_{p}, (1 < p < infinite)

Sung Guen Kim
경북대학교 자연과학대학 수학과|2008.09|Kyungpook Mathematical Journal|제48권 제3호|pp. 387-393

2

조회

0

다운로드

1

인용

0

참고문헌

주제분류수학

초록

In this note, we present some inequalities for the norm and numerical radius of 2-homogeneous polynomials from the 2-dimensional real space l^{2}_{p}, (1 < p < infinite) to itself in terms of their coefficients. We also give an upper bound for n^(k)(l^{2}_{p}) ), (k = 2, 3, · · · ).

Abstract

In this note, we present some inequalities for the norm and numerical radius of 2-homogeneous polynomials from the 2-dimensional real space l^{2}_{p}, (1 < p < infinite) to itself in terms of their coefficients. We also give an upper bound for n^(k)(l^{2}_{p}) ), (k = 2, 3, · · · ).

참고문헌 (17)

  1. F. F. Bonsall, "Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras" (1971), London Math. Soc. Lecture Note Ser. 2, Cambridge Univ. Press
  2. F. F. Bonsall, "Numerical Ranges II" (1973), London Math. Soc. Lecture Note Ser. 10, Cambridge Univ. Press
  3. H. F. Bohnenblust, "Geometrical properties of the unit sphere in Banach algebra", Ann. of Math, 62, pp.217~229 (1955)
  4. Y. S. Choi, "The polynomial numerical index of a Banach space", Proc. Edinburgh Math. Soc, 통권 : 49, pp.39~52 (2006)
  5. S. Dineen, "Complex Analysis on Infinite Dimensional Spaces" (1999), Springer-Verlag, London
  6. J. Duncan, "The numerical index of a normed space", J. London Math. Soc, 2, pp.481~488 (1970)
  7. E. Ed-dari, "On the numerical index of Banach spaces", Linear Algebra and Appl, 403, pp.86~96 (2005)
  8. C. Finet, "Numerical index and renorming", Proc. Amer. Math. Soc, 131, pp.871~877 (2003)
  9. B. M. Glickfeld, "On an inequality of Banach algebra geometry and semi-inner product space theory", Illinois J. Math, 14, pp.76~81 (1970)
  10. K. E. Gustafsan, "Numerical Ranges. The Field of Values of Linear Operators and Matrices" (1997), Springer, New York
  11. L. A. Harris, "Bounds on the derivatives of holomorphic functions of vectors, Colloque d´analyse, Rio de Janeiro", L. Nachbin Act, 1367, pp.145~163 (1975)
  12. V. Kadets, "Recent progress and open questions on the numerical index of Banach spaces", Rev. R. Acad. Cien. Serie A. Mat, 2000, pp.155~182 (2006)
  13. S. G. Kim, "On the polynomial numerical index of the real spaces c0, l1 and l1", J. Math. Anal. Appl, 337, pp.98~106 (2008)
  14. G. Lumer, "Semi-inner-product spaces", Trans. Amer. Math. Soc, 100, pp.29~43 (1961)
  15. G. Lopez, "Real Banach spaces with numerical index 1", Bull. London Math. Soc, 31, pp.207~212 (1999)
  16. M. Martin, "servey on the numerical index of Banach space", Extracta Math, 15, pp.265~276 (2000)
  17. M. Martin, "Numerical index of vector-valued function spaces", Studia Math, 142, pp.269~280 (2000)

이 간행물의 다른 논문 (16건)

Enumeration of Algebraic Tangles with Applications to Theta- curves and Handcuff GraphsHiromasa Moriuchipp. 337-357On Generalized Integral Operator Based on Salagean OperatorHuda Abdullah Al-Kharsanipp. 359-366Some Fixed Point Theorems for Multivalued Maps Satisfying an Implicit Relation on Metrically Convex SpacesDuran Turkoglu, Ishak Altunpp. 367-377Some properties of a Certain family of Meromorphically Univalent Functions defined by an Integral OperatorRasoul Aghalarypp. 379-385A Chemotherapy-Diffusion Model for the Cancer Treatment and Initial Dose ControlKhaled Mmohamed Saad, Hamdy Ibrahim Abdel-Gawadpp. 395-410
원문 보기