Category:Spectra (Bounded Linear Operators)
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This category contains results about spectra in the context of bounded linear operators.
Definitions specific to this category can be found in Definitions/Spectra (Bounded Linear Operators).
Let $\struct {X, \norm \cdot_X}$ be a Banach space over $\C$.
Let $A : X \to X$ be a bounded linear operator.
Let $\map \rho A$ be the resolvent set of $A$.
Let:
- $\map \sigma A = \C \setminus \map \rho A$
We say that $\map \sigma A$ is the spectrum of $A$.
Pages in category "Spectra (Bounded Linear Operators)"
The following 12 pages are in this category, out of 12 total.
S
- Spectral Theorem for Compact Hermitian Operators
- Spectrum of Adjoint of Bounded Linear Operator
- Spectrum of Bounded Linear Operator contains Point Spectrum
- Spectrum of Bounded Linear Operator equal to Spectrum as Densely-Defined Linear Operator
- Spectrum of Bounded Linear Operator is Closed
- Spectrum of Bounded Linear Operator is Compact
- Spectrum of Bounded Linear Operator is Non-Empty
- Spectrum of Bounded Linear Operator on Finite-Dimensional Banach Space is equal to Point Spectrum
- Spectrum of Compact Linear Operator on Infinite-Dimensional Banach Space contains Zero
- Spectrum of Self-Adjoint Bounded Linear Operator is Real and Closed
- Spectrum of Self-Adjoint Bounded Linear Operator is Real and Closed/Proof 1
- Spectrum of Self-Adjoint Bounded Linear Operator is Real and Closed/Proof 2