منابع مشابه
Norms of Positive Operators on LP-Spaces
Let 0 < T: LP(Y, v) -+ Lq(X, ) be a positive linear operator and let HITIP ,q denote its operator norm. In this paper a method is given to compute 1Tllp, q exactly or to bound 11Tllp q from above. As an application the exact norm 11VIlp,q of the Volterra operator Vf(x) = fo f(t)dt is computed.
متن کاملLINEAR OPERATORS ON Lp FOR 0
If 0 < p < 1 we classify completely the linear operators T: Lp -X where X is a p-convex symmetric quasi-Banach function space. We also show that if T: LLo is a nonzero linear operator, then forp < q < 2 there is a subspace Z of Lp, isomorphic to Lq, such that the restriction of T to Z is an isomorphism. On the other hand, we show that if p < q < o, the Lorentz space L(p, q) is a quotient of Lp ...
متن کاملLp-INVERSE THEOREM FOR MODIFIED BETA OPERATORS
and B(v+1,n) being the beta function (see, e.g., [3]). It is easily verified that the operators Bn are linear positive operators. Also, Bn(1,x) = 1. It turns out that the order of approximation for the operators (1.1) is at best O(n−1) howsoever smooth the function may be. With the aim of improving the order of approximation, we have to slack the positive condition of these operators for which ...
متن کاملEstimates in Lp for Magnetic Schrödinger Operators
We study the magnetic Schrödinger operator H(a,V ) in R, n ≥ 3. The L (1 < p < ∞) and weak-type (1,1) estimates are obtained under certain conditions, given in terms of the reverse Hölder inequality, on the magnetic field B = curl a and the electrical potential V . In particular, we show that the L and weak-type (1,1) estimates hold if the components of a are polynomials, and V is a nonnegative...
متن کاملOperator space embedding of Lq into Lp
The idea of replacing functions by linear operators, the process of quantization, goes back to the foundations of quantum mechanics and has a great impact in mathematics. This applies for instance to representation theory, operator algebra, noncommutative geometry, quantum and free probability or operator space theory. The quantization of measure theory leads to the theory of Lp spaces defined ...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 1976
ISSN: 0024-6107
DOI: 10.1112/jlms/s2-14.2.333