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Useful resources for examples

Fermat

Active member
Nov 3, 2013
188
I am doing a project on concepts like compact sets, compact operators, where I need examples in spaces like l_p, C[a,b]. When I look on google, there is mostly just theory, and the few examples there are are usually in R. Does anyone know good websites or books that have examples. Thanks.
 

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,702
I am doing a project on concepts like compact sets, compact operators, where I need examples in spaces like l_p, C[a,b]. When I look on google, there is mostly just theory, and the few examples there are are usually in R. Does anyone know good websites or books that have examples. Thanks.
A good example of a compact operator is the Volterra integral operator.

For interesting examples of compact sets, you probably need to look at non-metric topologies. For example, the unit ball of $l_p$ ($1<p<\infty)$ is compact in the weak*-topology.