On certain uniformly open multilinear mappings

DOI10.1215/17358787-3599741zbMath1356.46014OpenAlexW2392182131MaRDI QIDQ306998

Ehrhard Behrends, Marek Balcerzak, Filip Strobin

Publication date: 1 September 2016

Published in: Banach Journal of Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.bjma/1463153912

zbMATH Keywords

multiplicationuniformly open mapping\(L_{p}\) spacesmultilinear functionals

Mathematics Subject Classification ID

Special maps on topological spaces (open, closed, perfect, etc.) (54C10) Classical Banach spaces in the general theory (46B25) (Spaces of) multilinear mappings, polynomials (46G25) Linear relations (multivalued linear operators) (47A06) Forms (bilinear, sesquilinear, multilinear) (47A07)

Related Items (6)

When is multiplication in a Banach algebra open? ⋮ Multiplication in the space of functions of bounded variation ⋮ Nonlinear open mapping principles, with applications to the Jacobian equation and other scale-invariant PDEs ⋮ Where is matrix multiplication locally open? ⋮ Topological properties of operations on spaces of differentiable functions ⋮ Where is pointwise multiplication in real $CK$-spaces locally open?

Cites Work

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• Openness of multiplication in some function spaces
• An open mapping theorem without continuity and linearity
• A counterexample to the closed graph theorem for bilinear maps
• Points of openness and closedness of some mappings
• Products of n open subsets in the space of continuous functions on [0,1]
• A connection between multiplication in C(X) and the dimension of X
• An Elementary Counterexample to the Open Mapping Principle for Bilinear Maps
• Multiplying balls in the space of continuous functions on [0,1]

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