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        "quote": "所以若 $A-\\lambda I$ 是可逆的，我们就称复数 $\\lambda$ 是希尔伯特空间 $\\mathcal{H}$ 上的有界算子 $A$ 的<u id=\"concept-13-regular-value\" class=\"concept-term\" data-concept-identity=\"urn:uuid:3c19d901-1c08-4e84-a9c5-1658b4447b88\" data-concept-route=\"/concept-identities#concept-3c19d901-1c08-4e84-a9c5-1658b4447b88\">正则值(regular value)</u>， 此时$(A-\\lambda I)^{-1}$ 也存在并且有界。 $A$ 的<u id=\"concept-13-spectrum\" class=\"concept-term\" data-concept-identity=\"urn:uuid:6e3eb528-17bf-469f-92c2-4bd54698e28d\" data-concept-route=\"/concept-identities#concept-6e3eb528-17bf-469f-92c2-4bd54698e28d\">谱(spectrum)</u> $\\Sigma(A)$ 定义成 $A$中 的那些不是正则值的$\\lambda(\\in\\mathbb{C})$的集合。如果 $\\lambda$ 是 $A$ 的特征值，则如上所述，可以验证它在 $A$ 的谱中，反之则不然。这些特征值通常称为<u id=\"concept-13-point-spectrum\" class=\"concept-term\" data-concept-identity=\"urn:uuid:c768f687-a6f9-4e14-977a-488822437d2a\" data-concept-route=\"/concept-identities#concept-c768f687-a6f9-4e14-977a-488822437d2a\">点谱(point spectrum)</u>。谱中的其他点称为<u id=\"concept-13-continuous-spectrum\" class=\"concept-term\" data-concept-identity=\"urn:uuid:517e06c6-f907-4d3f-92ca-d3b6f06a4dba\" data-concept-route=\"/concept-identities#concept-517e06c6-f907-4d3f-92ca-d3b6f06a4dba\">连续谱(continuous spectrum)</u>。在这种情况下，可以想象$(A-\\lambda I)^{-1}$存在但无界。更常见的情形是，$(A-\\lambda I)^{-1}$只存在于 $\\mathcal{H}$ 的稠密域上，并且在该域上是无界的。我们将把这个问题留到13.6 节再讨论。",
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