diff --git a/narwhals/_spark_like/dataframe.py b/narwhals/_spark_like/dataframe.py
index c6d95f833..101d5ad24 100644
--- a/narwhals/_spark_like/dataframe.py
+++ b/narwhals/_spark_like/dataframe.py
@@ -52,7 +52,7 @@ def __native_namespace__(self) -> Any:  # pragma: no cover
     def __narwhals_namespace__(self) -> SparkLikeNamespace:
         from narwhals._spark_like.namespace import SparkLikeNamespace
 
-        return SparkLikeNamespace(  # type: ignore[abstract]
+        return SparkLikeNamespace(
             backend_version=self._backend_version, version=self._version
         )
 
diff --git a/narwhals/_spark_like/expr.py b/narwhals/_spark_like/expr.py
index b88919ff4..a8cafccfd 100644
--- a/narwhals/_spark_like/expr.py
+++ b/narwhals/_spark_like/expr.py
@@ -59,7 +59,7 @@ def __narwhals_namespace__(self) -> SparkLikeNamespace:  # pragma: no cover
         # Unused, just for compatibility with PandasLikeExpr
         from narwhals._spark_like.namespace import SparkLikeNamespace
 
-        return SparkLikeNamespace(  # type: ignore[abstract]
+        return SparkLikeNamespace(
             backend_version=self._backend_version, version=self._version
         )
 
@@ -139,7 +139,7 @@ def __ne__(self, other: SparkLikeExpr) -> Self:  # type: ignore[override]
 
     def __add__(self, other: SparkLikeExpr) -> Self:
         return self._from_call(
-            lambda _input, other: _input + other,
+            lambda _input, other: _input.__add__(other),
             "__add__",
             other=other,
             returns_scalar=False,
@@ -147,7 +147,7 @@ def __add__(self, other: SparkLikeExpr) -> Self:
 
     def __sub__(self, other: SparkLikeExpr) -> Self:
         return self._from_call(
-            lambda _input, other: _input - other,
+            lambda _input, other: _input.__sub__(other),
             "__sub__",
             other=other,
             returns_scalar=False,
@@ -155,16 +155,50 @@ def __sub__(self, other: SparkLikeExpr) -> Self:
 
     def __mul__(self, other: SparkLikeExpr) -> Self:
         return self._from_call(
-            lambda _input, other: _input * other,
+            lambda _input, other: _input.__mul__(other),
             "__mul__",
             other=other,
             returns_scalar=False,
         )
 
-    def __lt__(self, other: SparkLikeExpr) -> Self:
+    def __truediv__(self, other: SparkLikeExpr) -> Self:
         return self._from_call(
-            lambda _input, other: _input < other,
-            "__lt__",
+            lambda _input, other: _input.__truediv__(other),
+            "__truediv__",
+            other=other,
+            returns_scalar=False,
+        )
+
+    def __floordiv__(self, other: SparkLikeExpr) -> Self:
+        def _floordiv(_input: Column, other: Column) -> Column:
+            from pyspark.sql import functions as F  # noqa: N812
+
+            return F.floor(_input / other)
+
+        return self._from_call(
+            _floordiv, "__floordiv__", other=other, returns_scalar=False
+        )
+
+    def __pow__(self, other: SparkLikeExpr) -> Self:
+        return self._from_call(
+            lambda _input, other: _input.__pow__(other),
+            "__pow__",
+            other=other,
+            returns_scalar=False,
+        )
+
+    def __mod__(self, other: SparkLikeExpr) -> Self:
+        return self._from_call(
+            lambda _input, other: _input.__mod__(other),
+            "__mod__",
+            other=other,
+            returns_scalar=False,
+        )
+
+    def __ge__(self, other: SparkLikeExpr) -> Self:
+        return self._from_call(
+            lambda _input, other: _input.__ge__(other),
+            "__ge__",
             other=other,
             returns_scalar=False,
         )
@@ -177,6 +211,45 @@ def __gt__(self, other: SparkLikeExpr) -> Self:
             returns_scalar=False,
         )
 
+    def __le__(self, other: SparkLikeExpr) -> Self:
+        return self._from_call(
+            lambda _input, other: _input.__le__(other),
+            "__le__",
+            other=other,
+            returns_scalar=False,
+        )
+
+    def __lt__(self, other: SparkLikeExpr) -> Self:
+        return self._from_call(
+            lambda _input, other: _input.__lt__(other),
+            "__lt__",
+            other=other,
+            returns_scalar=False,
+        )
+
+    def __and__(self, other: SparkLikeExpr) -> Self:
+        return self._from_call(
+            lambda _input, other: _input.__and__(other),
+            "__and__",
+            other=other,
+            returns_scalar=False,
+        )
+
+    def __or__(self, other: SparkLikeExpr) -> Self:
+        return self._from_call(
+            lambda _input, other: _input.__or__(other),
+            "__or__",
+            other=other,
+            returns_scalar=False,
+        )
+
+    def __invert__(self) -> Self:
+        return self._from_call(
+            lambda _input: _input.__invert__(),
+            "__invert__",
+            returns_scalar=self._returns_scalar,
+        )
+
     def abs(self) -> Self:
         from pyspark.sql import functions as F  # noqa: N812
 
diff --git a/narwhals/_spark_like/namespace.py b/narwhals/_spark_like/namespace.py
index d34867b00..56cc4d271 100644
--- a/narwhals/_spark_like/namespace.py
+++ b/narwhals/_spark_like/namespace.py
@@ -16,6 +16,7 @@
 
     from narwhals._spark_like.dataframe import SparkLikeLazyFrame
     from narwhals._spark_like.typing import IntoSparkLikeExpr
+    from narwhals.dtypes import DType
     from narwhals.utils import Version
 
 
@@ -67,6 +68,28 @@ def col(self, *column_names: str) -> SparkLikeExpr:
             *column_names, backend_version=self._backend_version, version=self._version
         )
 
+    def lit(self, value: object, dtype: DType | None) -> SparkLikeExpr:
+        if dtype is not None:
+            msg = "todo"
+            raise NotImplementedError(msg)
+
+        def _lit(_: SparkLikeLazyFrame) -> list[Column]:
+            import pyspark.sql.functions as F  # noqa: N812
+
+            return [F.lit(value).alias("literal")]
+
+        return SparkLikeExpr(  # type: ignore[abstract]
+            call=_lit,
+            depth=0,
+            function_name="lit",
+            root_names=None,
+            output_names=["literal"],
+            returns_scalar=True,
+            backend_version=self._backend_version,
+            version=self._version,
+            kwargs={},
+        )
+
     def sum_horizontal(self, *exprs: IntoSparkLikeExpr) -> SparkLikeExpr:
         parsed_exprs = parse_into_exprs(*exprs, namespace=self)