Abstract
Our approach to zLpd (zero Lie product determined) Banach algebras and zJpd (zero Jordan product determined) Banach algebras will be essentially different from the purely algebraic approach to zLpd and zJpd algebras in Part I. We will first study continuous bilinear functionals φ with the property that xy = yx = 0 implies φ(x, y) = 0 and then apply the obtained results to show that, under certain additional assumptions, zpd Banach algebras are also zLpd and zJpd Banach algebras. This is roughly the concept of the chapter, although we will make several digressions.
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Brešar, M. (2021). Zero Lie/Jordan Product Determined Banach Algebras. In: Zero Product Determined Algebras. Frontiers in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-80242-4_6
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DOI: https://doi.org/10.1007/978-3-030-80242-4_6
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