Multi-view clustering is a powerful technique for improving analytical performance by fusing complementary multi-source information. However， there are deficient in two ways： It neglects the strong inherent correlation between representation tensors and affinity matrices， and the separate two-step strategy of representation learning and clustering leads to lack of association between these processes， rendering inefficient in handling missing data， noise and outliers in multi-view data processing. In order to address these issues， this paper proposes a multi-view sub-space clustering method based on tensor low-rank learning. A methodology is put forward for the analysis of high-order correlations among data points and the identification of the intrinsic structure of the data. The method involves the introduction of a high-order tensor constraint based on low-rank representation （LRR） and the adoption of tensor nuclear norm minimization （TNNM） based on tensor singular value decomposition （t-SVD）. This approach facilitates the transformation of the original non-convex optimization problem into a solvable convex one. The application of an adaptive weighted Schatten-p norm has been utilized to capture the inherent differences between singular values， with the assistance of their prior information. Spectral clustering has been integrated into a unified framework for the purpose of optimizing the affinity matrix， with a view to more effectively characterizing clustering structures. The inexact augmented Lagrange multiplier （ALM） method has been utilized to decompose the model into four solvable sub-problems for the purpose of efficient optimization. Comprehensive experiments are conducted on six benchmark datasets spanning facial images， news stories， handwritten digits and general objects， with systematic optimization of key parameters to ensure reliability. The findings demonstrate that the proposed method exhibits a substantial enhancement in performance when compared to four contemporary algorithms， namely t-SVD-MSC， ETLMSC， WTNNM and MLAN. The proposed method demonstrated an accuracy of 0.981 on the Yale dataset， 0.995 on the UCI-Digits dataset， and 0.971 on the Scene-15 dataset. The proposed method effectively increases the robustness of the affinity matrix against noise and outliers. It accurately extracts the intrinsic subspace structure of multi-view data and demonstrates excellent practical performance and strong generalization ability in the analysis of high-dimensional and incomplete multi-view data.