Viṣṇu — The All-Pervading Supreme Person
Viṣṇu (from the Sanskrit root viś = to pervade, to enter everywhere; Viṣṇu = the one who pervades everything) is one of the oldest and most central names of the Supreme Being in the Vedic and Āgamic traditions. The Ṛg Veda names Viṣṇu as the one who 'strides across' the cosmos in three steps (tri-vikrama), a cosmic act interpreted in Śrī Vaiṣṇava tradition as Bhagavān's encompassment of all three realms — this world, the intermediate space, and the transcendent Śrī Vaikuṇṭham.
Viṣṇu in Viśiṣṭādvaita: Rāmānujāchārya's philosophy explains Viṣṇu's pervasion not as an abstract omnipresence but as śarīrī-śarīra-bhāva — the jīvas (souls) and jagat (matter) are the body (śarīra) of Viṣṇu, who is their inner self (antaryāmin). This pervasion is not pantheistic; Viṣṇu remains distinct from and transcendent over His body of souls and matter, even as He pervades and controls them from within.
The Viṣṇu Gāyatrī and Liturgical Use: The Viṣṇu Gāyatrī mantra (Oṃ nārāyaṇāya vidmahe vāsudevāya dhīmahi tanno viṣṇuḥ pracodayāt) uses all three names together — Nārāyaṇa, Vāsudeva, and Viṣṇu — reflecting the Vedic understanding that they refer to the same Supreme Person from different angles: Nārāyaṇa as the ground of all nāras, Vāsudeva as the one who dwells in all, and Viṣṇu as the pervader.
Viṣṇu in the Divya Prabandham: The Āzhvārs sing of Viṣṇu throughout the 4,000 pāsurams. Tirumazhisai Āzhvār's Nānmugan Tiruvantādi and Periyāzhvār's Tirumozhi celebrate His pervasion as the ground of bhakti — He is the one who fills the universe and the heart of the devotee simultaneously. The Viṣṇu Sahasranāma (1,000 divine names) opens and centres on Viṣṇu as the primary referent.