In this chapter and the next we focus on bases and basis-like systems in Hilbert spaces. Our goal in this chapter is to understand bounded unconditional bases in Hilbert spaces, but in order to do this, we first need to study sequences that need not be bases but which do have a property that is reminiscent of Bessel’s Inequality for orthonormal bases. These Bessel sequences will also be very useful to us in Chapter 8 when we consider frames in Hilbert spaces

Unable to display preview. Download preview PDF.

Authors and Affiliations

1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

   Christopher Heil

Corresponding author

Correspondence toChristopher Heil.

Reprints and permissions

© 2011 Birkhäuser Boston

Policies and ethics