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Special operator ideals
Extremal ellipsoids determined by ideal norms
More about q rsumming operators
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2-summing 2)-summing norms argument assume Banach lattice Banach-Mazur distance cogradations completes the proof concludes the proof convex Corollary cotype q defined denote diagonal operator dim F dimensional gradation dual Dvoretzky's theorem ellipsoid en(Z Euclidean norm factorization Figiel finite sequence finite-dimensional Banach spaces finite-dimensional subspace follows formal identity operator functions Gaussian Hausdorff space Hilbert space ideal norms implies inequality infimum interpolation invariant isometric isomorphism K-convex Lemma let u e Lp-factorable matrix maximal volume Moreover n-dimensional Banach space normed operator ideal numbers operator norm operators acting orthogonal matrix orthogonal projection orthonormal basis p-nuclear p-summing operators particular Pelczynski Pietsch Pisier positive integer Proof Let proof of Theorem properties proved r)-summing Rademacher Rademacher functions resp result satisfies scalars shows space and let subset subspace symmetric spaces Tomczak-Jaegermann u e L(E ultraproduct unit ball unit vector basis unitary ideals universal constant vector basis