@highergeometer@mathstodon.xyz
2026-03-12 01:38 UTC
RE: https://mathstodon.xyz/@nbourbaki/116209443910251750
No way! Here's a machine translation of the contents of the two new chapters (which, incidentally, are finally covering the material Grothendieck did in his PhD in the 50s!)
"This new fascicle of the Book on Topological Vector Spaces is devoted to tensor products of locally convex spaces, as well as their applications.
Chapter VI presents the theory of topological tensor products. It introduces the notion of a tensor construction, which equips the tensor product of locally convex spaces with a locally convex topology. The properties of two tensor constructions, called minimal and maximal, are detailed, along with their uses in describing certain common function spaces. The chapter continues with a study of dualities and envelopes of tensor constructions, followed by a proof of Grothendieck's fundamental inequality.
Chapter VII opens with a study of nuclear maps between locally convex spaces, whose properties are analogous to those of operators defined by continuous kernels. It examines notions of trace and determinant for nuclear maps between Banach spaces. Finally, the class of nuclear spaces is presented, which combines several of the themes of this volume."
Replies (0)
No replies.