Chapter 10 Spectral theorems for bounded self-adjoint operators on a Hilbert space
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چکیده
Let H be a Hilbert space. For a bounded operator A : H → H its Hilbert space adjoint is an operator A∗ : H → H such that 〈Ax, y〉 = 〈x,A∗y〉 for all x, y ∈ H. We say that A is bounded self adjoint if A = A∗. In this chapter we discussed several results about the spectrum of a bounded self adjoint operator on a Hilbert space. We emphasize that in this chapter A is bounded, there is also a notion of unbounded self adjoint operator which we will discuss in subsequent chapters.
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