Bilinear Derivation in Banach Spaces

Abstract We study the bilinear functor $$\mathfrak B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> </mml:math> that associates to a Banach space X the Banach space $$\mathfrak B(X)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> of scalar bilinear bounded forms on X . We obtain its injective and projective derivatives, compute its projective and injective stabilization and introduce and compute its coprojective and coinjective stabilizations.