Reply to Gelfand and Cleveland

Reply to Gelfand et al and Solla.

TO THE EDITOR—We appreciate the interest Gelfand et al [1] have shown regarding our observational, nonrandomized, comparative multicenter study [2]. Infec-tive endocarditis (IE) is an uncommon, severe disease [3], and it is inevitable that randomized trials on this condition are lacking. In our observational study, the combination of ampicillin and ceftriax-one (AC) was compared with the standa...

Reply to Gelfand et al and Solla

TO THE EDITOR—We appreciate the interest Gelfand et al [1] have shown regarding our observational, nonrandomized, comparative multicenter study [2]. Infective endocarditis (IE) is an uncommon, severe disease [3], and it is inevitable that randomized trials on this condition are lacking. In our observational study, the combination of ampicillin and ceftriaxone (AC) was compared with the standard...

Gelfand pairs

Let K ⊂ G be a compact subgroup of a real Lie group G. Denote by D(X) thealgebra of G-invariant differential operators on the homogeneous space X = G/K. ThenX is called commutative or the pair (G,K) is called a Gelfand pair if the algebra D(X)is commutative. Symmetric Riemannian homogeneous spaces introduced by Élie Cartanand weakly symmetric homogeneous spaces introduced by Sel...

Gelfand numbers and widths

In general, the Gelfand widths cn(T ) of a map T between Banach spaces X and Y are not equivalent to the Gelfand numbers cn(T ) of T . We show that cn(T ) = cn(T ) (n ∈ N) provided that X and Y are uniformly convex and uniformly smooth, and T has trivial kernel and dense range. c ⃝ 2012 Elsevier Inc. All rights reserved.

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