# Hilbert modules over function algebras by R. G. Douglas, V.I. Paulsen

By R. G. Douglas, V.I. Paulsen

**Read Online or Download Hilbert modules over function algebras PDF**

**Similar algebra & trigonometry books**

**An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra**

During this creation to commutative algebra, the writer choses a direction that leads the reader during the crucial rules, with no getting embroiled in technicalities. he is taking the reader fast to the basics of complicated projective geometry, requiring just a uncomplicated wisdom of linear and multilinear algebra and a few uncomplicated workforce thought.

**Inequalities : a Mathematical Olympiad approach**

This ebook is meant for the Mathematical Olympiad scholars who desire to organize for the research of inequalities, an issue now of common use at numerous degrees of mathematical competitions. during this quantity we current either vintage inequalities and the extra beneficial inequalities for confronting and fixing optimization difficulties.

This quantity offers the lawsuits of the foreign convention on ""Recent growth in Algebra"" that was once held on the Korea complex Institute of technological know-how and know-how (KAIST) and Korea Institute for complicated learn (KIAS). It introduced jointly specialists within the box to debate growth in algebra, combinatorics, algebraic geometry and quantity thought.

- Precalculus: Real Mathematics, Real People
- Nest Algebras
- Rings and Things and a Fine Array of Twentieth Century Associative Algebra
- Numbers, groups, and codes

**Extra resources for Hilbert modules over function algebras**

**Example text**

Since we can choose the same / throughout a neighbourhood of any given point t, and mf is continuous, the new function (j) is continuous. It is bounded by ||ra||. Given h G £2(T) of finite support, we can choose / such that / = 1 on supp/i, and then n((/))h = ji(mf)h = mfi(f)h = mh. Thus m — /x(0) is in fi{Cb{T)), as required. • In view of the above, it is natural to speculate on the multiplier algebra of Co(T,JC(H)). A naive guess might be Cb(T,B(H)), but for infinite-dimensional H this algebra is too small.

Then A n l = q(Xnl + Lan) —> q(T). Since CI is always closed, q(T) = XI for some A G C. Then (An - A)l + L a n -> T - Al G ker

We want to build a representation of A. The underlying vector space will be X 0 H^, and the inner product will be characterized by ( x 0 / i I y®k) := (7r((y , x) )h\k). (2,25) To see where this comes from, consider the case B = C. 25) is (y , x)c(h \k) = {x\ y)(h I k). 23) on the tensor product of Hilbert spaces. 64. 25). 25). 59. 25) is bilinear in (x, /i), and hence defines a linear map / y <8>/fc : XoWfr -> C. Then (y, k) i-> fy®fk is bilinear from X x Hn to (X©H*)", hence gives a linear map L on X 0 7 ^ , and we define (a \ (3) := L@(a).