Live briefing
Everything about Projective tensor product
In functional analysis, an area of mathematics, the projective tensor product of two locally convex topological vector spaces is a natural topological vector space structure on their tensor product. Namely, given locally convex topological vector spaces and, the projective topology, or π-topology, on is the strongest topology which makes a locally convex topological vector space such that the canonical map is continuous. When equipped with this topology, is denoted and called the projective tensor product of and. It is a particular instance of a topological tensor product. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Projective tensor productA 5-minute orientation
- Skim a recent paper: Daugavet property in projective symmetric tensor products of Banach spacesInfluential work since 2022
- Pick up a classic book: TensorsThe most-reprinted book on the subject
- Read the landmark paper: Cofiniteness conditions, projective covers and the logarithmic tensor product theoryCited 58 times
- Go sideways: Nuclear spaceA closely related topic
- Go sideways: Injective tensor productA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Cofiniteness conditions, projective covers and the logarithmic tensor product theory
OBSERVATIONS ABOUT THE PROJECTIVE TENSOR PRODUCT OF BANACH SPACES, I—
The projective tensor product of Fréchet-Montel spaces
Operator space projective tensor product of $C^*$-algebras
Projective tensor products of $C^*$-algebras.
Weakly open sets in the unit ball of the projective tensor product of Banach spaces
Schauder decompositions and the Fremlin projective tensor product of Banach lattices
IDEALS IN OPERATOR SPACE PROJECTIVE TENSOR PRODUCT OF C*-ALGEBRAS
🆕 Influential since 2022
Daugavet property in projective symmetric tensor products of Banach spaces
Geometric analysis of the pseudo-projective curvature tensor in doubly and twisted warped product manifolds
Impact of pseudo-projective curvature tensor on sequential doubly warped product manifolds with physical applications
Pseudo-projective Tensor on Sequential Warped Products
Doubly warped product manifolds: Investigations through the projective curvature tensor and relativistic applications
📚 Books worth reading
- 📕TensorsJ. M. Landsberg · 2011
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Nuclear space In mathematics, nuclear spaces are topological vector spaces that can be viewed as a generalization of finite-dimensional Euclidean spaces and share many…
- Injective tensor product In functional analysis, an area of mathematics, the injective tensor product is a particular topological tensor product, a topological vector space (TVS)…
- Topological tensor product In mathematics, there are usually many different ways to construct a topological tensor product of two topological vector spaces. For Hilbert spaces or…
- Glossary of functional analysis This is a glossary for the terminology in a mathematical field of functional analysis. Throughout the article, unless stated otherwise, the base field…
- Inductive tensor product The finest locally convex topological vector space (TVS) topology on X ⊗ Y , {\displaystyle X\otimes Y,} the tensor product of two locally convex TVSs…
- Metrizable topological vector space In functional analysis and related areas of mathematics, a metrizable (resp. pseudometrizable) topological vector space (TVS) is a TVS whose topology is…
- Nuclear operator In mathematics, nuclear operators are an important class of linear operators introduced by Alexander Grothendieck in his doctoral dissertation. Nuclear…
- Auxiliary normed space In functional analysis, a branch of mathematics, two methods of constructing normed spaces from disks were systematically employed by Alexander Grothendieck…