Isometric embeddings of finite-dimensional $\ell_p$-spaces over the quaternions

DOI10.1090/S1061-0022-04-00842-8zbMath1076.46005OpenAlexW1502020166MaRDI QIDQ4675544

Oksana A. Shatalova, Yuri I. Lyubich

Publication date: 4 May 2005

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-04-00842-8

zbMATH Keywords

isometric embeddingscubature formulasaddition theorem

Mathematics Subject Classification ID

Isometric theory of Banach spaces (46B04) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21)

Related Items (8)

Asymptotically optimal designs on compact algebraic manifolds ⋮ Upper bound for isometric embeddings ℓ₂^{𝑚}→ℓ_{𝑝}ⁿ ⋮ On isometric embedding ℓpm→S∞ and unique operator space structure ⋮ Topologically projective, injective and flat modules of harmonic analysis ⋮ Isometric embeddability of \(S_q^m\) into \(S_p^n\) ⋮ Topologically flat Banach modules ⋮ On tight projective designs ⋮ Lower bounds for projective designs, cubature formulas and related isometric embeddings

Cites Work

• t-designs in projective spaces
• Isometric embeddings between classical Banach spaces, cubature formulas, and spherical designs
• Spherical t-designs which are orbits of finite groups
• On tight t-designs in compact symmetric spaces of rank one
• Averaging sets: A generalization of mean values and spherical designs
• Spherical codes and designs
• Subspaces of \(L_p\) isometric to subspaces of \(\ell_p\)
• Chebyshev-type quadrature on multidimensional domains
• Problems in algebraic combinatorics
• Spherical harmonics
• Spherical Harmonics and Integral Geometry on Projective Spaces
• Sums of even powers of real linear forms
• Bounds for quaternionic line systems and reflection groups.
• The Addition Formula for Jacobi Polynomials and Spherical Harmonics
• Waring's Problem
• Euclidean subspaces of the complex spaces \(\ell_p^n\) constructed by orbits of finite subgroups of \(SU(m)\)
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