Wong, Landis2020-02-262020-02-262020-02-262020-01-082020-01-092020-02-26http://hdl.handle.net/1993/34550In this thesis we will study the notions of bounded pseudo-amenability and bounded pseudo-contractibility for a Banach algebra, where we require a Banach algebra to possess a multiplier bounded approximate diagonal or a multiplier bounded central approximate diagonal. We will investigate various properties of these types of Banach algebras, including: l^p-direct sums, relationships to unitizations, hereditary properties on ideal and quotient subalgebras, connections to other generalized notions of amenability, and projective tensor products of these Banach algebras. We will also provide some examples of boundedly pseudo-amenable and boundedly pseudo-contractible Banach algebras.engMathematicsFunctional analysisAmenabilityContractibilityBanach algebrasBounded pseudo-amenabilityBounded pseudo-contractibilitymaster thesis