Matrix subspaces of L₁

• Autorzy: Gideon Schechtman
• Języki publikacji: EN

Abstrakty

EN

If $E = {e_{i}}$ and $F = {f_{i}}$ are two 1-unconditional basic sequences in L₁ with E r-concave and F p-convex, for some 1 ≤ r < p ≤ 2, then the space of matrices ${a_{i,j}}$ with norm $||{a_{i,j}}||_{E(F)} = ||∑_{k}||∑_{l} a_{k,l}f_{l}||e_{k}||$ embeds into L₁. This generalizes a recent result of Prochno and Schütt.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B45: Banach sequence spaces
• 46B15: Summability and bases

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 215
• Numer: 3
• Strony: 281-285

Daty

wydano

2013

Twórcy

autor

Gideon Schechtman

• Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel

Identyfikatory

DOI

10.4064/sm215-3-5