Multiplier algebras of Lp-operatoralgebras

It is known that the multiplier algebra of an approximately unital and nondegenerate L p -operator algebra is again an L p -operator algebra.In this paper we investigate examples that drop both hypotheses.In particular, we show that the multiplier algebra of T p 2 , the algebra of strictly upper triangular 2 2 matrices acting on p 2 , is still an L p -operator algebra for any p.To contrast this result, we first provide a thorough study of the augmentation ideal of 1 (G) for a discrete group G.We use this ideal to define a family of nonapproximately unital degenerate L p -operator algebras, F p 0 ,)3/( whose multiplier algebras cannot be represented on any L q -space for any q [1, ) as long as p [1, p 0 ] [ p 0 , ), where p 0 = 1.606 and p 0 is its Hlder conjugate.