Hilbert Spaces
Orthogonality, Riesz representation, and compact self-adjoint operators.
Hilbert Spaces. Orthogonality, Riesz representation, and compact self-adjoint operators.
Foundations and canonical references
The standard treatments of hilbert spaces approach the subject from complementary angles. Halmos, Introduction to Hilbert Space and the Theory of Spectral Multiplicity (1957) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Conway, A Course in Functional Analysis (1990) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for hilbert spaces include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1957Introduction to Hilbert Space and the Theory of Spectral Multiplicityhalmos-1957
- textbook · primary · 1990A Course in Functional Analysisconway-1990
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